9. Given similar triangles ABC and PQR with AB = 4 and PQ = 7. Fill in the following chart stating the scale factor, ratio of perimeters,
and ratio of areas:

Given:

Similar triangles ABC and PQR with AB = 4 and PQ = 7.

To find:

The scale factor, ratio of perimeters, and ratio of areas.

Solution:

In similar figures the scale factor is the ratio of side or image and corresponding side of original figure.

In similar triangles ABC and PQR, the scale factor is

The scale factor of triangle ABC to triangle PQR is .

The ratio of the perimeters of similar triangles is equal to the ratio of their corresponding sides.

The ratio of the perimeters is 4:7.

The ratio of the areas of similar triangles is equal to the ratio of squares of their corresponding sides.

Therefore, the ratio of the areas is 16:49.