EXAMPLE 4 Find perimeters of similar figures Swimming A town is building a new swimming pool. An Olympic pool is rectangular with length 50 meters and width 25 meters. The new pool will be similar in shape, but only 40 meters long. Find the scale factor of the new pool to an Olympic pool. a.

EXAMPLE 4 Find perimeters of similar figures Find the perimeter of an Olympic pool and the new pool. b. SOLUTION Because the new pool will be similar to an Olympic pool, the scale factor is the ratio of the lengths, a. 40 50 = 4 5

Find perimeters of similar figures EXAMPLE 4 Find perimeters of similar figures The perimeter of an Olympic pool is 2(50) + 2(25) = 150 meters. You can use Theorem 6.1 to find the perimeter x of the new pool. b. x 150 4 5 = Use Theorem 6.1 to write a proportion. x = 120 Multiply each side by 150 and simplify. The perimeter of the new pool is 120 meters. ANSWER

GUIDED PRACTICE for Example 4 In the diagram, ABCDE ~ FGHJK. 4. Find the scale factor of FGHJK to ABCDE. The scale factor is the ratio of the length is ANSWER 15 10 = 3 2

In the diagram, ABCDE ~ FGHJK. GUIDED PRACTICE for Example 4 In the diagram, ABCDE ~ FGHJK. 5. Find the value of x. SOLUTION You can use the theorem 6.1 to find the perimeter of x x 18 10 15 = Use Theorem 6.1 to write a proportion. 15 x = 18 10 Cross product property. x = 12

GUIDED PRACTICE for Example 4 ANSWER The value of x is 12

GUIDED PRACTICE for Example 4 In the diagram, ABCDE ~ FGHJK. 6. Find the perimeter of ABCDE. SOLUTION As the two polygons are similar the corresponding side lengths are similar To find the perimeter of ABCDE first find its’ side lengths.

GUIDED PRACTICE for Example 4 To find AE FG AB = FK AE 15 10 = 18 x Write Equation 15 10 = 18 x Substitute 15x = 180 Cross Products Property x = 12 Solve for x AE = 12

GUIDED PRACTICE for Example 4 To find ED FG AB = KJ ED 15 10 = y Write Equation 15 10 = y Substitute 15y = 150 Cross Products Property y = 10 Solve for y ED = 10

GUIDED PRACTICE for Example 4 To find DC FG AB = HJ CD 15 10 = 12 z Write Equation 15 10 = 12 z Substitute 15z = 120 Cross Products Property z = 8 Solve for z DC = 8

GUIDED PRACTICE for Example 4 To find BC FG AB = GH BC 15 10 = 9 a Write Equation 15 10 = 9 a Substitute 15a = 90 Cross Products Property a = 6 Solve for x BC = 6

GUIDED PRACTICE for Example 4 The perimeter of ABCDE = AB + BC + CD + DE + EA = 10 + 6 + 8 + 10 + 12 = 46 ANSWER The perimeter of ABCDE = 46