c Substitute the values into the rewritten formula.
A
a P=2x + 2 π r
B
b x=1/2P-Ï€ r
C
c 173 feet
Practice makes perfect
a The perimeter of the given figure is made up of two sides and two semicircles. The two sides each have a length of x, and the two semicircles make up a circle with a radius r. To find their length, let's substitute the radius into the formula for the circumference of a circle.
C = 2 π rNow that we have the circumference of the circle, we can write the perimeter of the entire figure, which is a sum of all the sides.
Perimeter: x + x+ 2 π r
Let's simplify the expression by adding like terms.
x + x + 2 π r ⇔ 2x+2 π r
b In order to solve the formula for x, we need to isolate x on one of the sides.
c The perimeter is given as 660 feet and the radius of the half circles is given as 50 feet. By substituting these values into the formula from Part B we can find x.
