Question

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

Answer 1

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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