Question

14. Find the length of the longest rod which can fit into a cuboidal box with height 7 cm and the length of the
diagonal of the base of the box which has a rectangular shape is 24 cm.​

Answer 1

Given,

Height of the box = 7 cm

Diagonal of the base = 24 cm

To find,

The length of the longest rod that can fit in that box.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

The longest distance in a cuboid is the diagonal of the cuboid.

Now,if we visualise the whole situation, then we will find that the height, diagonal of the base and diagonal of the cuboid forms a right angle triangle. Here, the diagonal of the cuboid will be the hypotenuse and thus we can apply the Pythagoras theorem to calculate it's length.

Length of the diagonal of the cuboid box

= √(Height)² + (Base diagonal)²

= √(7)²+(24)²

= √(49+576)

= √625

= 25 cm (approx)

Hence, the length of the longest rod will be 25cm.