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?

1 Answer
Jul 16, 2017

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