Question

The perimeter of a semicircle is 108 cm. What is the perimeter of the square
drawn on the diameter of the semicircle ?..
(1) 168 cm2) 84 cm (3) 252 cm (4) 294 cm
explain woth the help of figure.​

Answer 1

$\huge\underline\bold\orange{Answer:-}$

$\large\underline\bold\red{Given:-}$

• Perimeter of a Semicircle = 108cm .

$\large\underline\bold\red{To\:find:-}$

• The Perimeter of a Square .

$\large\underline\bold\red{Formula\:used:-}$

• Perimeter of a semicircle is$\dashrightarrow$$\large\bold\red{πr+2r}$

$\large\underline\bold\red{Solution:-}$

$\implies$$\frac{22}{7} \times r + \: 2r \: = \: 108$

$\implies$$\frac{(22r + 14r)}{7} = \: 108$

$\implies$$36r \: = \: 108 \times 7$

$\implies$$r \: = \frac{108 \times 7}{36}$

$\implies$$r \: = \: 3 \times 7$

$\implies$$r \: = 21cm$

$\small\bold\red{Therefore,\:Diameter\:=\:42cm}$

• Perimeter of a square is 4 times diameter , 4×42 = 168cm

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Answer 2

Step-by-step explanation:

$We \: know \: that,$

$Perimeter \: of \: semicircle =\pi r + 2r = 108 \: cm$

$r(\pi + 2) = 108$

$r( \frac{22}{7} + 2) = 108$

$r( \frac{22 + 14}{7} ) = 108$

$r( \frac{36}{7} ) = 108$

$r = \not 108\times \frac{7}{ \not36}$

$r = 3 \times 7$

$r = 21 \: cm$

$Now \: we \: also \: know \: that$

$Diameter = 2r \: = > 2 \times 21 = > 42 \: cm$

$Perimeter \: of \: square = 4 \times side$

$4 \times 42 = 168 \: cm$