Question

The ratio of corresponding side lengths are 1:3. the perimeter of the smaller triangle is 36 inches. the area of the smaller triangle is 54 square inches. What is the perimeter and area of the larger figure?

Answer 1

See explanation.

Explanation:

The ratio of the side lengths is `1:3`, so all sides of the larger triangle are 3 times larger than the sides of the smaller one. Therfore the perimeter of the larger triangle is also 3 times larger. It is: `3xx36=108` inches.

There is a theorem which says:

The ratio of areas of a similar figures equals the square of the ratio of the similarity.

In the example the ratio of the similarity is `3`, therfore the larger triangle has `3^2=9` times larger area:

`A_2=9xxA_1=9xx54=486` square inches