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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
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B
No
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Solution

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 cm
And, perimeter is the sum of all the 4 sides, so the side of the square will be =524=13 cm


Similarly, for the triangle,


Perimeter =39 cm
Equilateral triangles have all side lengths equal.
Therefore, the side length 393=13 cm

So, for both the cases, the diameter of the circle will be =13 cm

The circles will be congruent to each other.


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