McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
1. Circles and Circumference
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Exercise 50 Page 722

Use the circumference formula to find the value of x.

KJ=24

Practice makes perfect

Let's take a look at the given diagram.

We are given that the sum of the circumferences is 56Ï€. Using this information we can write an equation. 56Ï€=C_K+C_J+C_H Let's recall that the circumference of a circle is twice the product of its radius and pi. 56Ï€=2Ï€ r_k+2Ï€ r_J+2Ï€ r_H By substituting appropriate values for the radii of the circles we can find the value of x.

56Ï€=2Ï€ r_k+2Ï€ r_J+2Ï€ r_H
56Ï€=2Ï€ * 4x+2Ï€ * 2x+2Ï€ * x
â–¼
Solve for x
56Ï€=2Ï€(4x+2x+x)
28=4x+2x+x
28=7x
7x=28
x=4

The value of x is 4. Using this value we can evaluate KJ. Notice that KJ is the sum of the radii of ∘ K and ∘ J.

KJ= 4x+ 2x
KJ=6x
KJ=6* 4
KJ=24