Question

Find the length of a box with b = 16 cm, h = 12 cm and the length of the longest rod that fits in the box is 29 cm.

Answer 1

Given that:

The longest rod that fits in the box is 29 cm and b = 16 cm, h = 12 cm

We know that,

The longest rod that can be placed in a room is nothing but its diagonal.

The diagonal of a cuboid is `sqrt(l^2 + b^2 + h^2)`, where l is the length, b is the breadth and h is the height of the cuboid.

Then,

`29 = sqrt(l^2 + 16^2 + 12^2)`

Squaring both the sides, we get,

29² = l² + 16² + 12²

841 = l² + 256 + 144

l² = 841 – 400

l² = 441

l = 21 cm

Therefore, the length of a box is 21 cm.