Math, asked by chocohaeun0805, 8 months ago

In the figure, the perimeter of the shaded region is 12π cm. Find the value of x.

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Answers

Answered by ButterFliee
3

GIVEN:

  • The perimeter of the shaded region is 12π cm.

TO FIND:

  • What is the value of x ?

SOLUTION:

We know that, the perimeter of the shaded region is 12π

We have to find the value of 'x'

We know that, the Circumference of the semicircle is:- \bf{ \frac{2 \pi r}{2} }

\bf{\star \: Circumstance = \pi r \: \star }

Diameter of larger semicircle = (x + x) cm

\rm{ Radius = \frac{Diameter}{2} = \frac{2x}{2}}

\bf{ \star \: Radius = x \: cm \: \star }

 The radius of larger semicircle is x cm 

Diameter of smaller semicircle = x cm

\rm{ Radius = \frac{Diameter}{2} = \frac{x}{2}}

\bf{\star \:  Radius = \frac{x}{2} \: cm \: \star }

❛ The radius of smaller semicircle is x/2 cm ❜

According to question:-

On putting the given values in the formula, we get

\rm{\mapsto \pi x  - \pi \frac{x}{2} + \pi \frac{x}{2} = 12 \pi }

\rm{\mapsto \pi x = 12 \pi }

\bf{\mapsto \: \star \: x  = 12 \: \star }

Radius = 12 cm

❛ Hence, the value of x is 12 cm ❜

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