If the ratio of the perimeter of two similar triangles is then what is the ratio of the area?
Calculate ratio of area of triangles
Given, ratio of perimeter of the triangles is .
Let, , , and be the sides of the the smaller triangle, and , , and be the corresponding sides of the bigger triangle. Then,
[Since they are similar triangles]
where is the proportionality constant
We are given that,
The area of similar triangles is directly proportional to the square of the ratio of the corresponding sides. Thus,
Therefore, the ratio of the area of the given similar triangles is .