Question

The perimeter of a square is equal to the
perimeter of a rectangle of length 42 cm
and breadth 60 cm. Find the
circumference of a semicircle whose
diameter is equal to the side of the
square.
Select one:​

Answer 1

Answer:

here is the step by step explanation of the answer.

Answer 2

Given :-

Perimeter of square =Perimeter of rectangle

Length of rectangle=42cm

Breadth 60

To find

The circumference of semicircle whose diameter is equal to the side of square

Now A.T.Q

$\underline{\dag{\sf{\: Perimeter\:of \: rectangle=2(l+b)}}}$

=> Perimeter =2(42+60)

=> Perimeter of rectangle =2× 102

=> Perimeter of rectangle= 204cm

So perimeter of square is also 204cm

Now the side of square

$\underline{\dag{\sf{\: Perimeter\:of \: square=4\times side}}}$

$\sf\implies 4\times side =204\\ \\ \sf\implies side =\cancel{\dfrac{204}{4}}\\ \\ \sf\implies Side= 51$

• So the diameter of semi circle is 51 cm

Now the circumference of semicircle

$\underline{\dag{\sf{\: Circumference\:of\: semicircle=\pi r+2r}}}$

$\sf\implies Radius=\dfrac{Diameter}{2}\\ \\ \sf\implies {\red{Radius =\dfrac{51}{2}}}$

• Now the circumference of semicircle

$\sf\implies Circumference=\dfrac{\cancel{22}}{7}\times \dfrac{51}{\cancel{2}} +\cancel{2}\times \dfrac{51}{\cancel{2}}\\ \\ \sf\implies Circumference=\dfrac{11\times 51}{7}+51\\ \\ \sf\implies Circumference=\dfrac{561+51\times 7}{7}\\ \\ \sf\implies Circumference=\dfrac{561+357}{7}\\ \\ \sf\implies Circumference=\cancel{\dfrac{918}{7}}\\ \\ \sf\implies Circumference=131.14cm$

$\boxed{\sf{\dag{\:\: Circumference\:of\: semicircle=131.14cm}}}$