Lenny Conundrum

Every week, The Neopets Team releases a new Lenny Conundrum puzzle, and each week that puzzle gets posted on our blog. You can discuss with others the answer in the comments and come up with a solution! We also discuss the Mystery Picture Answers aswell!

Click Below to Buy Neopoints

Click Below to <b>Buy Neopoints</b>
Buy Neopoints at the lowest prices from our trusted partner for Neopets.
For a limited time, use the discount code : "BABYPB" when you make a purchase to recieve a free Baby Paint Brush with the purchase of anything $50+ (Enter in the code when you enter your username).

Wednesday, October 12, 2011

Lenny Conundrum - Round #424

Arty loves to garden! In fact, he has quite a large one in the back of his shop that he keeps all to himself. It's 55 yards wide and 40 yards long with a diagonal path, one yard wide, running through it. Erm... maybe this will help:




Okay, so, it's not to scale. Arty's a gardener, not an architect! Anyway, he'd like to cover the path with some nice pebbles, but he's unsure of how much he'll need to buy. First he needs to know how big the path is!

What is the area of the path?
Enter the number in square yards, rounding to the nearest whole number.

76 comments :

  1. Diagonal of a rectagle= square root of side squared + side squared. The squares and the square root sign cancel out so it' 44+ 50. So it
    's 94ft long?

    ReplyDelete
  2. Use Pythagorean's Theorem. (a^2)+(b^2) = c^3.
    (55^2)+(40^2) = c^2.
    c^2 = 68.007
    ROUND TO NEAREST WHOLE NUMBER AND LEAVE ANSWER IN SQUARE YARDS
    So, the answer would be:
    68 square yards

    ReplyDelete
  3. Pythag is for triangles.

    ReplyDelete
  4. OH LOL I GET IT THE TRIANGLE IN THE RECTANGLE.

    but doesn't it matter how wide it is?

    ReplyDelete
  5. and there are 2 equal triangles which are 55 x 40 x 68

    ReplyDelete
  6. If you submit the correct answer right now, what are the chances you won?

    ReplyDelete
  7. but it is a parallellogram as well?

    ReplyDelete
  8. I got 68 square yards as well. I know I didn't make it in time though(so even if my answer is wrong, I'm not too hung up over it).

    ReplyDelete
  9. isn't 68 yards implying the distance of the hypotenuse length but not the AREA...?

    ReplyDelete
  10. area of square minus area of 2 triangles

    55*40-54*40=40

    ReplyDelete
  11. It is NOT 68. The height of the triangle is indeed 40, but is the base 55? Check again. You'll see that the Pythagorean formula is not applicable here (though it IS necessary in some part of this calculation). If you've taken Geometry, you should have enough knowledge to solve this, though it's pretty hard (it's a conundrum after all).

    ReplyDelete
  12. how does one write square yard?
    square yard?
    sq yd?
    yd²?
    yd2?

    X 3X

    ReplyDelete
  13. I think 40 is right - the rectangle has an area of 2200, each triangle has an area of 1080. 2200-1080-1080=40.

    The left over area is the path.

    ReplyDelete
  14. Let's see: The whole area measure 55*40 and consider that the triangles are (1/2)54*40. Thus, the area covered by triangles is 54*40, so the area to be covered is 55*40-54*40 which is 40. Simple, really. Too bad I only got home right now

    ReplyDelete
  15. Haha. It is 40. You just solve for the area of a parallelogram (40 times 1 yard = 40).

    ReplyDelete
  16. Look at the pathway as a parallelogram. Find the diagonal section by using the Pythagorean theorem, but MAKE SURE that you do 55-1 because that 55 includes the 1 yard that is the width of the path. So the actual base of the triangle is 54, not 55. If you find the diagonal and use that to find the area of the parallelogram, you will find the area of the path.

    55-1=54
    (54^2)+(40^2)=c^2
    c^2=4516
    c=67.201 (This is the diagonal length)
    67.201*1(width of path)=67.201 square yards.
    Round the decimal. Answer is 67.

    ReplyDelete
  17. I thought that to calculate the area of a parallelogram you had to multiply the base with the height, not the length of the side...

    ReplyDelete
  18. 132

    ((55-1)+40)/2*V2





    how big the path is
    ^ this is what he wants

    ReplyDelete
  19. 50 is the answer.
    Take the Pythagorean Theorem to find the triangle within the side corner, approximate the two side rectangles within the edge of the path, and you get 50. Simple. Oh dear I might be wrong though.

    ReplyDelete
  20. It's 68. Use the phythagorean theorem to find the base of the parallelogram. It's 68.007. We already know the path is 1 yard wide, so that's be the height. b*h=a. 68.007*1+68.007. Round up. 68 square yards!

    ReplyDelete
  21. Wow you guys are making this waaay too difficult. Use the pythag to find that 40^2 + 55^2 gives you 4625. Square root is the base of the parallelo, then times the height which is one as denoted by the statement. Calm yourselves lol!

    ReplyDelete
  22. HAHAHA
    None of you got it correct yet.
    Keep trying, n00bs.

    ReplyDelete
  23. I'll let you guys know when one of you get it right.

    ReplyDelete
  24. (55)(40) - x = \sqrt{x^2 - 40^2} (40)=67

    ReplyDelete
  25. Why are people using 55-1 as a side? 1 is the width of the path, once it reaches the 55 side, the path is at an angle to the side. that means the side of the triangle is less than 54, because the length of the path along the side is greater than 1.

    ReplyDelete
  26. Wow. So many wrong answers. But there's one correct too. Most of you really suck at this, don't you?

    ReplyDelete
  27. 40 lol area of parallelogram is base x height
    1 x 40= 40

    ReplyDelete
  28. 68 square yards

    ReplyDelete
  29. You are making it so difficult!
    The area of the whole garden is 55 × 40 = 2200 yards. The area beside the path is a triangle so we calculate this area: 0,5((55-1)×40)) = 1080. Now, we have 2 triangles, so it is 1080 × 2 = 2160. Triangle + triangle + path = garden area, therefore 2160 + path = 2200, therefore gardenarea - 2triangles = path, so 2200 - 2160 = 40. I hope you guys get it now ;)! No parallelogram calculation needed lol.

    ReplyDelete
  30. I like how you act like the parallelogram calculation is hard. It's just base times height. 1 yard x 40 yards = 40 yards^2. As you can see, both answers are correct, but this way was much easier lol.

    ReplyDelete
  31. It is hard. The base isn't 1 and the height isn't 40 either. The height is very very small and the base is like 67..

    ReplyDelete
  32. I hope you guys realize that the 55 including the path, which means you don't have to subtract anything. Thats just making the path shorter. And your answer too small. And to those of you using the 2 triangle/ parallelogram approach, the end of the path that is along the 55 yard side is longer than 1. You don't have enough information to figure out how long it actually is without using trig. The answer is 68.

    ReplyDelete
  33. Ahhhh nevermind it's wrong, it's 67

    ReplyDelete
  34. 1/sinus(45) gets something like 1.4, 55-1.6=53.6 then 53.6²+40²=4471
    squareroot= 66.86= 67, which is the base,
    times height which is 1 = still 67.

    ReplyDelete
  35. the answer is 57 I think...

    It would make sense: the small side from the 55, is square root 2 = 1.414... (since you can see a smaller triangle there, with both sides being 1)

    So then two ways to calculate: Area of parallellogram => base * height = 1.414... * 40 = 56.5 = 57

    Whole area minus the two triangles =>
    (55 *40) - ((55-1.414...)* 40) = 56.5 = 57

    This is only true if the other side from the smaller traingle is also 1, which I am not entirely sure of. But since it's a parallel diagnol I think this is case.

    ReplyDelete
  36. Lol nevermind it's 67. Found a way to calculate it three times, abc-formula and all that jazz. Worked a lot better lol.

    ReplyDelete
  37. Lol nevermind it isn't.

    ReplyDelete
  38. The path isn't 1 yard wide at the end, it's √2 wide.

    ReplyDelete
  39. Once you understand this picture, you will also understand that it is 57

    http://tinypic.com/r/2zrdc1e/7

    ReplyDelete
  40. The guy who said 66.66666 (so 67) is right. Like I said, the large triangles are 40 yards by a little less than 55 yards. Hint: Use similar triangles.

    ReplyDelete
  41. 2*(a+b)= 2*(55+40)=190

    ReplyDelete
  42. The triangles are 40*53,6=2144 and the whole area 40*55=2200. I don't know how you get 67 out of it...

    ReplyDelete
  43. how did you get 53,6?

    ReplyDelete
  44. I typed in 68 and it told me it was correct. Simple Pythagorus. 55*55= 3 025 40*40=1600
    add them together you get 4625. You just then square root it and *1. I did wonder how so may people got it wrong, then I saw this board

    ReplyDelete
  45. XD Lenny Conundrum told you it was correct? 53,5858 comes from the fact that the path is 1 yard wide and 1,4142 wide at the end.

    ReplyDelete
  46. FINALLY!!

    Yep, the answer is 53,6585 = 54!

    ReplyDelete
  47. Finally I mean, I thought no one would get it right like me xD

    ReplyDelete
  48. Learn simple maths and then come online to complain! the answer is 57. You saw it proved above.

    ReplyDelete
  49. I know simple math and I am pretty sure it's 54.

    ReplyDelete
  50. I will be laughing my ass off, when they tell you it's 57. Or 56 if TNT screws up the rounding up again.

    ReplyDelete
  51. Pythagoras is not needed for this exceedingly simple problem. You can either tae the entire rectangle and substract the two triangles or look at the path as the paralellogram it is. Both methods will yield you 40, the correct answer.

    ReplyDelete
  52. There is no way it even could be 40. The path is clearly longer than the 40 yard long side. If the path was 40 square yards, it would have to be 40 yards long as it is stated that it's 1 yard wide.

    ReplyDelete
  53. 40 sounds plausible in hindsight, but it is not. Though 57 sounds odd, it has a better chance of winning than 40. Oh well, hoping my early submission of 67 does the trick.

    ReplyDelete
  54. YOU GUYS ARE IDIOTS!!!!! First of all, i think the 40 theory sounds most logical to me and also it says to enter your number in SQUARE YARDS therefore the answer should be 40 sq. yds.

    ReplyDelete
  55. You guys are making this WAY MORE COMPLICATED than it actually is...

    ReplyDelete
  56. Let me answer this for you. The area of the entire rectangle is 2200. (55x40=2200)

    To figure out the area of the path, you must figure out the area of both triangles. Given that the path is one yard wide, the base and height of both triangles is 54 and 40... so you just need to multiply 54 by 40 and subtract that from 2200. (yes the area of a triangle is 1/2(b*h) but both triangles are the same size so its unnecessary to divide by half and add them together)

    The answer is 40sq. yards. 2200-2160=40

    ReplyDelete
  57. Otherwise correct, but the base of the triangle IS NOT 54!

    http://tinypic.com/r/2zrdc1e/7

    As you can see in this picture the red line is the mentioned one yard. The blue line is therefore the squareroot of two. Which makes the base of the triangle 53.5858 yards.

    40*53.5858=2143.432
    2200-2143.432=56.568=57

    ReplyDelete
  58. I still go with my answer of 57 (56.5)

    I hope I win a bigger loot this round. I was the first one to reply to this thread with 57 as an answer. Lol.

    ReplyDelete
  59. Answer is 67 or (66.6666666)

    Formulas Needed: Pythagoras and area of a parallelogram

    Lets call the little section from the side 55 as "X" an unknown value

    40^2 + (55-X)^2 = 40X^2 (40x because parallelogram is base x Height, we know the height of 40 but no base.) That = X^2 - 110X + 4625 = 1600X^2

    Rearrange by taking them all on the left across = 1599X^2 +100X - 4625 = 0

    Now the Quadratic Formula

    -B ± (Square root)/b^2-(4AC)
    ---------------------------
    (2 x A)

    Therefore: =
    ______________________
    -110x ± √110^2 - (4x1599x-4625)
    --------------------------------- = 5/3 or 1.67
    (2 x 1599)

    x= 1.6666666 so (55-x) = (55 - 1.66666) = 53.333

    Last but not least pythagoras as 1 yard would not affect the area from the hypotenuse of the triangle= 53.333^2 + 40^2 = 4444.44444 then square root 4444.4444 = 66.66666666 rounder up = 67!!!

    Peace ^^

    ReplyDelete
  60. 40^2 + (55-X)^2 = 40X^2

    ^ I have no idea what you are calculating with this? 40x would be the area of the path, not the length of the hypotenuse.

    ReplyDelete
  61. Okay it's either 68 or 67 or 40. 68/67 I gathered from using pythagoras theorem and then multiply by the width (1) which left 68. However, I realised that the triangle is NOT actually 55 long... the path is 1 yard wide so it is actually 54.

    So, I got 67 that way.

    Then I realised that the path is not a rectangle so you can't just use the worked out sides and times it by 1.. (can you?)

    Sooo what I did is worked out the added areas of both triangles 2( 1/2 * 40 * 54 )and then that answer subtracted from the total area of the entire garden. So, what is left is the area of the path.
    However, neopets say 'round to the nearest number' so yeah...

    ReplyDelete
  62. TNT is assuredly wrong. The answer is DEFINITELY 67 (200/3, or 66.66666...). Some of the answers above have complete explanations for it being 67.

    How do we tell them they're wrong?

    ReplyDelete
  63. Seriously... is this just a case of "life isn't fair?"

    ReplyDelete
  64. It's a case of sometimes people screw the heck up.

    ReplyDelete
  65. 64?!?!?!? Are they insane?! How did they come up with that?!

    ReplyDelete
  66. OH! Maybe the path is 1 meter wide PERPENDICULAR to the path. We were all using the idea that the path is 1 meter wide parallel to the sides of the garden. If you do the math that way, then instead of the path being 1 meter "wide", you have to use a right triangle with arctan(40/55) and one leg being one meter wide, so you'd have to figure the area of the path using a width of 1/cos(arctan(40/55))=1.23649. Which means the path should have an area of...
    49.46?

    Somebody want to double-check my math? I thought I had this cracked, but apparently not.

    ReplyDelete
  67. Its 67, my friend and I used autocad on this and that cannot be wrong.

    ReplyDelete