Perimeter of Backyard: 130feet Perimeter of Patio: 52feet
Practice makes perfect
We want to put a rectangular patio in our backyard similar to the shape of our backyard. We have been told that our backyard is 45 feet long and 20 feet wide. Our new patio will be 18 feet long. This can be modeled in the following diagram.
We want to find the perimeters of the patio and backyard. Let's start with the perimeter of the backyard.
Perimeter of the Backyard
We know that the perimeter of a rectangle is twice the length plus twice the width of the rectangle. Since we know the length and width of the backyard, we can find its perimeter, P_B, as follows.
P_B&=2(45)+2(20)
&=130
Therefore, the perimeter of the backyard is 130 feet.
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
Since the length of the patio corresponds to the length of the backyard, using this theorem we can write the following proportion.
P_P/130=18/45
Next, we will solve the proportion for P_P to find the perimeter of the patio.
