Question

A square is inscribed inside a square ABCD such that the vertices of the smaller square lies on the midpoints of the sides of the square ABCD. Find the ratio of the area of the square ABCD to that of the smaller one.

• A. 2
• B. 3
• C. 4
• D. 5
• E. 8

Answer 1

The correct option is A

2

Let the side length of the square ABCD be `x'

Area of the square ABCD = a${}^2$

Side length of the smaller square = $\frac{a}{\sqrt{2}}$

Area of the smaller square = $\frac{a^2}{2}$

Ratio of the areas = 2