ΔABC ∼ ΔPQR. The perimeters of ΔABC and ΔPQR are 72 cm and 43.2 cm, respectively. What is the ratio of the area of ΔABC to the area of ΔPQR ?

25 : 9

We know that,

The ratio of perimeter of two triangles is equal to the ratio to its corresponding sides and we also know that the ratio of area of two similar triangles is always equal to the square of its corresponding sides.

So in this question ratio of perimeter is given that is also the ratio of its corresponding sides,

Ratio of sides = 72 : 43.2

= 5 : 3

So the ratio of the area of these triangles = 5² : 3²

So the ratio of the area of these triangles = 25 : 9