Question

what is radius of circle which touches all the sides of the square internally when the perimeter of square is 60 cm

Answer 1

Perimeter of sq = 4a

Answer 2

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$\underline{SOLUTION}$ ➡

$Given ,\\ \\ Perimeter \: \: of \: \: the \: \: square \: = 60 \: \: cm \\ \\ Let, \: \: \\ \\ Sides \: \: of \: \: the \: \: square \: = a \\ \\ So, \\ \\ Perimeter \: \: of \: \: the \: \: square \: = 4a \\ \\ \\ A.T.Q., \\ \\ \: \: \: \: \: \: \: 4a = 60 \: \: cm \\ \\ = > \: a = \frac{60}{4} \: \: cm\: \\ \\ = > a = 15 \: \: \: cm \\ \\ \\ Therefore \\ \\ Sides \: \: of \: \: the \: \: square \: = 15 \: \: cm$

$Now, \\ \\ Radius \: \: of \: \: the \: \: circle ,\:R = \frac{a}{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{15}{2} \: \: \: cm \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 7.5\: \: \: cm\: \:$

$\underline{ANSWER}$ ➡

$\boxed{\bold{Sides\: \: of\: \: the \: \: square , \: a = 15\: \: cm}}$

$\boxed{\bold{Radius \: \: of \: \: the \: \: circle , \: R = 7.5 \: \: cm}}$

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