Exercise 4 Page 454

We are given two similar triangles. They have a pair of corresponding sides of length 12 meters and 8 meters.

We are asked to find the perimeter and the area of the smaller triangle knowing the perimeter and the area of the larger triangle. To do it, we will first find a scale factor k of the larger triangle to the smaller triangle. k=8/12=2/3 A scale factor of 23 means that the length of each side of the smaller triangle is 23 times the length of the corresponding side of the larger triangle. This also implies that the perimeter of the smaller triangle is 23 times the perimeter of the larger triangle P_(smaller)=2/3P_(larger) The perimeter of the larger triangle is 48 meters. Let's calculate the perimeter of the smaller triangle. The perimeter of the smaller triangle is 32 meters. Next we will find its area. Recall that when two similar polygons have a scale factor of k, the ratio of their areas is equal to k^2. A_(smaller)/A_(larger)=(2/3)^2 The area of the larger triangle is 180 square meters. Let's substitute 180 for A_(larger) into the above expression and solve it for the are of the smaller triangle. The area of the smaller triangle is 80 square meters.