Question

A stick of length 19√2 cm was placed inside a cuboid box which is 5 cm wide and 11 cm high. If the size of the stick is maximum, then what is the length of the cuboid box?
1. 24 cm
2. 26 cm
3. 22 cm
4. 28 cm

Answer 1

Correct Answer - Option 1 : 24 cm

Given:

Length of stick = 19√2 cm

Width of box = 5 cm

Height of box = 11 cm

Concept used:

The length of max size stick placed inside the box is equal to the diagonal of the cuboid box.

Formula used:

Length of diagonal pf a cuboid = √(l² + b² + h²)

Calculation:

Let the length of the box = 'l' cm

∵ 19√2 = √(l2 + 52 + 112)

On squaring both sides;

⇒ 722 = l2 + 25 + 121

⇒ l2 = 722 - 25 - 121

⇒ l2 = 576 cm²

⇒ l = √576 cm

⇒ l = 24 cm

∴ Length of the box is 24 cm