Question

Find the height of a box if the longest rod that fits in the box is 21 cm and l = 20 cm, b = 5 cm.

Answer 1

Given that:

The longest rod that fits in the box is 21 cm and l = 20 cm, b = 5 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,

`21 = sqrt(20^2 + 5^2 + h^2)`

Squaring both the sides, we get,

(21)² = 20² + 5² + h²

441 = 400 + 25 + h²

h² = 16

h = 4 cm

Therefore, the height of a box is 4 cm.