Question

We have a square with perimeter $52$ cm and an equilateral triangle with perimeter $39$ cm. If two circles have its diameter equal to the side of the square and side of the triangle respectively. Will the circles be congruent?

• A. Yes
• B. No

Answer 1

The correct option is A Yes

Two circles are cut with diameter as the side of the square and side of the triangle, respectively, so we need to find the sides to analyse the circles.

For the square,


Perimeter $=52\text{cm}$
And, perimeter is the sum of all the $4$ sides, so the side of the square will be $=\frac{52}{4}=13\text{cm}$


Similarly, for the triangle,


Perimeter $=39\text{cm}$
Equilateral triangles have all side lengths equal.
Therefore, the side length $\frac{39}{3}=13\text{cm}$

So, for both the cases, the diameter of the circle will be $=13\text{cm}$

$\therefore$ The circles will be congruent to each other.