Exercise 32 Page 599

Let's begin with recalling what we know about the perimeters of similar polygons. If two polygons are similar, then their perimeters are proportional to the scale factor between them.We can use this information and create a proportion. Perimeter_1/Perimeter_2=Side_1/Side_2 By substituting 53.5 and 32.1 for the perimeters and 25 for the side length of the first garden, we can evaluate the side length of the second garden. Let x be this length.

Perimeter_1/Perimeter_2=Side_1/Side_2

SubstituteValues

Substitute values

53.5/32.1=25/x

CrossMult

Cross multiply

53.5* x=32.1*25

Multiply

Multiply

53.5x=802.5

DivEqn

.LHS /53.5.=.RHS /53.5.

x=802.5/53.5

CalcQuot

Calculate quotient

x=15

The length of the longest side of this garden is 15 feet.