Unluckily, last week I lost my measuring tape. It was unlucky as I had to measure Billy's toy box.
Luckily though I could remember that the top had an area of 720 square inches, the side was 800 square inches, and the end was 360 square inches.
What were the true dimensions of the toy box?
Puzzle Copyright © Kevin Stone
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Answer
Width=40, height=20, depth=18.
Reasoning
If we call the height H, the width W and the depth D we have:
H x W = 800
H = 800 ÷ W (1)
W x D = 720
W = 720 ÷ D (2)
H x D = 360
H = 360 ÷ D (3)
Using (1) and (3) we have:
800 360
——— = ———
W D
800 x D = 360 x W
Using (2):
800 x D = 360 x 720
———
D
800 x D2 = 259,200
D2 = 324
D = 18
Using (2), W = 40.
Using (1), H = 20.