Presentation on theme: "EXAMPLE 4 Find perimeters of similar figures Swimming"— Presentation transcript:
1 EXAMPLE 4Find perimeters of similar figuresSwimmingA 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.
2 EXAMPLE 4Find perimeters of similar figuresFind the perimeter of an Olympic pool and the new pool.b.SOLUTIONBecause the new pool will be similar to an Olympic pool, the scale factor is the ratio of the lengths,a.4050=45
3 Find perimeters of similar figures EXAMPLE 4Find perimeters of similar figuresThe perimeter of an Olympic pool is (50) + 2(25) = 150 meters. You can use Theorem 6.1 to find the perimeter x of the new pool.b.x15045=Use Theorem 6.1 to write a proportion.x = 120Multiply each side by 150 and simplify.The perimeter of the new pool is 120 meters.ANSWER
4 GUIDED PRACTICEfor Example 4In the diagram, ABCDE ~ FGHJK.4. Find the scale factor of FGHJK to ABCDE.The scale factor is the ratio of thelength isANSWER1510=32
5 In the diagram, ABCDE ~ FGHJK. GUIDED PRACTICEfor Example 4In the diagram, ABCDE ~ FGHJK.5. Find the value of x.SOLUTIONYou can use the theorem 6.1 to find the perimeter of xx181015=Use Theorem 6.1 to write a proportion.15 x=Cross product property.x = 12
6 GUIDED PRACTICEfor Example 4ANSWERThe value of x is 12
7 GUIDED PRACTICEfor Example 4In the diagram, ABCDE ~ FGHJK.6. Find the perimeter of ABCDE.SOLUTIONAs the two polygons are similar the corresponding side lengths are similar To find the perimeter of ABCDE first find its’ side lengths.
8 GUIDED PRACTICE for Example 4 To find AE FG AB = FK AE 15 10 = 18 x Write Equation1510=18xSubstitute15x = 180Cross Products Propertyx = 12Solve for xAE = 12
9 GUIDED PRACTICE for Example 4 To find ED FG AB = KJ ED 15 10 = y Write Equation1510=ySubstitute15y = 150Cross Products Propertyy = 10Solve for yED = 10
10 GUIDED PRACTICE for Example 4 To find DC FG AB = HJ CD 15 10 = 12 z Write Equation1510=12zSubstitute15z = 120Cross Products Propertyz = 8Solve for zDC = 8
11 GUIDED PRACTICE for Example 4 To find BC FG AB = GH BC 15 10 = 9 a Write Equation1510=9aSubstitute15a = 90Cross Products Propertya = 6Solve for xBC = 6
12 GUIDED PRACTICEfor Example 4The perimeter of ABCDE = AB + BC + CD + DE + EA== 46ANSWERThe perimeter of ABCDE = 46