Question

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:

Answer 1

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

`k=(PQ)/(AB)`

`k=(7)/(4)`

The scale factor of triangle ABC to triangle PQR is
`(7)/(4)`.

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

`\frac{\text{Perimeter of }\Delta ABC}{\text{Perimeter of }\Delta PQR}=(AB)/(PQ)`

`\frac{\text{Perimeter of }\Delta ABC}{\text{Perimeter of }\Delta PQR}=(4)/(7)`

`\frac{\text{Perimeter of }\Delta ABC}{\text{Perimeter of }\Delta PQR}=4:7`

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.

`\frac{\text{Area of }\Delta ABC}{\text{Area of }\Delta PQR}=(AB^2)/(PQ^2)`

`\frac{\text{Area of }\Delta ABC}{\text{Area of }\Delta PQR}=(4^2)/(7^2)`

`\frac{\text{Area of }\Delta ABC}{\text{Area of }\Delta PQR}=(16)/(49)`

`\frac{\text{Area of }\Delta ABC}{\text{Area of }\Delta PQR}=16:49`

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