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EXAMPLE 4

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. a. Find the scale factor of the new pool to an Olympic pool. EXAMPLE 4.

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EXAMPLE 4

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  1. 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. a. Find the scale factor of the new pool to an Olympic pool. EXAMPLE 4 Find perimeters of similar figures

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

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

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

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

  6. ANSWER The value ofxis12 for Example 4 GUIDED PRACTICE

  7. In the diagram, ABCDE ~ FGHJK. for Example 4 GUIDED PRACTICE 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.

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

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

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

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

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

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