7.2.2 Using Proportional Relationships (continued) Example 4 Using Ratios to Find Perimeters and Areas
If the similarity ratio of two similar figures is a b , then the ratio of their perimeters is , and the ratio
a b
2
2 2
⎞ ⎠ ⎟
⎛ ⎝ ⎜
a b
a b
, or
.
of their areas is
The perimeter is different by a simple multiplier, while the area is different by the square of the multiplier. The perimeter and area of a triangle are determined here using the Proportional Perimeters and Areas Theorem. The perimeter, area, and length of one side are given for a triangle that is similar to the example triangle. The length of the corresponding side of the unknown triangle is given. To determine the perimeter of the unknown triangle, set up a proportion with the ratio of the corresponding sides of the triangles and the ratio of the known perimeter to the unknown perimeter. Cross multiply and solve for the unknown perimeter. The unknown perimeter is found to be 45 ft. To determine the area of the unknown triangle, set up a proportion with the ratio of the squares of the corresponding sides of the triangles and the ratio of the known area to the unknown area. Cross multiply and solve for the unknown area. The unknown area is found to be 162 ft 2 .
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