Question

-. I have a box. The two dimensions of the box are 4 m and 3 m. Compute the third
dimension of the box so that the space diagonal of the box is an integer.
Space
[Hint: Pythagorean Triplets are ; n, -
22
diagonal
If n = 5 m, then (5)2 + (12)2 = (13)2
Here, 13 m will be space diagonal which is an integer.]
4 m​

Answer 1

third dimension of box = 12 cm

Step-by-step explanation:

The two dimensions of the box are 4 m and 3 m.

Let say third dimension is x

Then Diagonal = √(4)² + (3)² + x²

= √x² + 25

= √ x²  + 5²

Pythagorean triplets are  n , (n² - 1)/2  , (n² + 1)/2

Here n = 5

=> (n² - 1)/2  = (25 - 1)/2 = 24/2 = 12

(n² + 1)/2 = (25 + 1)/2 = 13

hence  x = 12   & diagonal = 13

third dimension of box = 12 cm

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