The window of the house is in the form of a rectangle surmounted by a semi-circular portion, having a perimeter of 10 m as shown in figure.

If x and y represent the length and breadth of rectangular region, then the perimeter of the window in terms of x is :

$x+2y +\frac{\pi x}{2}=10$

The correct answer is Option (3) → $x+2y +\frac{\pi x}{2}=10$

Given

$x+2y+\frac{πx}{2}=10⇒2x+4y+πx=20$

so $y=\frac{20-(π+2)x}{4}$

$x⇒x+2y +\frac{\pi x}{2}=10$