Question

Two shapes with equal perimeter are pictured below.

Answer 1

Answer:

Measure of CD = 17 units

Step-by-step explanation:

Perimeter of a polygon = Sum of measures of all sides of the polygon

Perimeter of the given rectangle = 2(length + width)

                                                       = 2[(x + 3) + (2x - 1)]

                                                       = 2(3x + 2) units

Perimeter of triangle EFG = EF + FG + GE

                                           = (x - 7) + (4x - 8) + (3x + 1)

                                           = (8x - 14)

                                           = 2(4x - 7) units

Since, perimeters of both the figures are equal,

2(3x + 2) = 2(4x - 7)

3x + 2 = 4x - 7

4x - 3x = 7 + 2

x = 9

Measure of CD = (2x - 1)

                         = 2(9) - 1

                         = 17 units