Exercise 37 Page 41

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 r

Now 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.

P=2x + 2 π r

SubEqn

LHS-2 π r=RHS-2 π r

P-2 π r= 2x

DivEqn

.LHS /2.=.RHS /2.

P-2 π r/2=x

WriteDiffFrac

Write as a difference of fractions

P/2-2 π r/2=x

SimpQuot

Simplify quotient

P/2- π r = x

MoveNumRight

a/b=1/b* a

1/2P- π r = x

RearrangeEqn

Rearrange equation

x=1/2P-π r

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.

x=1/2P-π r

SubstituteII

P= 660, r= 50

x=1/2( 660)-π( 50)

Multiply

x=1/2(660)-50 π

MoveRightFacToNumOne

1/b* a = a/b

x=660/2-50 π

SimpQuot

Simplify quotient

x=330-50π