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

1.	In the figure, the perimeter of the shaded region is 12π cm. Find the value of x.
Answer» 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 $\rm{\mapsto \pi x - \pi \frac{x}{2} + \pi \frac{x}{2} = <klux>12</klux> \pi }$ $\rm{\mapsto \pi x = 12 \pi }$ $\bf{\mapsto \: \star \: x = 12 \: \star }$ ∴ Radius = 12 cm ❛ Hence, the value of x is 12 cm ❜ ___________________