(Q3) Inner part of a cupboard is in the cuboidical shape with its length, breadth and height in the ratio 1 : √2 : 1. What is the angle made by the longest stick which can be inserted cupboard with its base inside?

Solution :

The ratio of the length, breadth and height = 1 : √2 : 1

Let its length be = x

breadth = √2 x height = x

The longest stick that can be placed on the base is along its hypotenuse

= √(l² + b²)

= √(x² + (√ x )²)

= √(x² + x²) = √(x²) = √ x

[!! Again, the longest stick that can be inserted in the cup board is along the line join of the bottom corn on with' its opposite top corner, i.e., along the hypotenuse of the right triangle formed by height of the cup board, hypotenuse of the base and the line join of bottom corner with its opposite top corner.

Length of the largest stick = √[(√ x)² + x²] = √(x² + x²) = √x² = x ]

Now the angle made by the largest stick be = θ

tan θ = tan °

∴ θ = °