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Unluckily, last week I lost my measuring tape. It was unlucky as I had to measure Daniel'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?

Width=40, height=20, depth=18.

If we call the height H, the width W and the depth D we have:

H x W = 800             (so H = 800 ÷ W)         (1)

W x D = 720             (so W = 720 ÷ D)         (2)

H x D = 360             (so 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. QED.

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