Regular polygon ABCDE is similar to regular polygon TUVWX. Side AB is 5x – 1, and side TU is 4x – 2. These sides are corresponding sides. If the ratio of the perimeter of polygon ABCDE to the perimeter of polygon TUVWX is 4:3, what is the perimeter of polygon ABCDE?

Question

Accepted Answer

Since AB and TU are corresponding sides of similar polygons, the ratio of AB to TU is equal to the ratio of the perimeter of ABCDE to the perimeter of TUVWX; AB:TU = 5x – 1 ⁄ 4x – 2 = 4 ⁄ 3 , 15x – 3 = 16x – 8, x = 5. Therefore, the length of AB is 5(5) – 1 = 25 – 1 = 24 units. Since ABCDE is a regular polygon with 5 sides, each of the 5 sides measures 24 units. Therefore, the perimeter of ABCDE is (5)(24) = 120 units.

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