Question

a square is inscribed in a circle of diameter d and another square is circumscribing the circle.find the ratio

Answer 1

I hope ,


it is a right answer

Answer 2

Answer:

2:1

Step-by-step explanation:

Given information: The diameter of the circle is d.

Area of square is

$Area=a^2$

where, a is the side length.

The side length of the outer square is d. So, the area of outer square is

$A_1=d^2$

The diagonal of the inner square is d.

According to the Pythagoras theorem,

$hypotenuse^2=perpendicular^2+base^2$

$d^2=a^2+a^2$

$d^2=2a^2$

$\frac{d^2}{2}=a^2$

So, area of the inner square is

$A_2=\frac{d^2}{2}$

We need to find the ratio of area of outer square to inner square.

$\dfrac{A_1}{A_2}=\dfrac{d^2}{\frac{d^2}{2}}$

$\dfrac{A_1}{A_2}=\dfrac{d^2}{1}\times \dfrac{2}{d^2}$

$\dfrac{A_1}{A_2}=\dfrac{2}{1}$

Therefore, the required ratio is 2:1.