Question

An isosceles right triangle is inscribed in a square. Its hypotenuse is a mid segment of the square. What is the ratio of the square’s area to the triangle’s area?

• A. 1:2
• B. 1:3
• C. 4:1
• D. none of these

Answer 1

The correct option is C 4:1

Graphical Division: -

Assume the square to have a side 2a. Hence, area of square = 4a${}^2$

Using graphical division, we can divide the figure into 8 parts as follows. The triangle in question is the shaded part

Thus the triangle is ${\frac{2}{8}}^{th}$ of the square area

Hence, required ratio = 4:1