Question

If the ratio of the perimeters of two triangles is 6 : 5, and the area of the larger triangle is 648 in2, what is the area of the smaller triangle?

Answer 1

area of smaller triangle = 450 in²

Explanation:

given the ratio of the perimeter of 2 triangles = a : b , then

ratio of their areas = a² : b²

here the ratio of the perimeters = 6 : 5 , then

raio of areas = 6² : 5² = 36 : 25

let x be the area of the smaller triangle then by proportion

`(ratio)/(area)`

`(36)/(648)` =
`(25)/(x)` ( cross- multiply )

36x = 648 × 25 = 16200 ( divide both sides by 36 )

x = 450

area of smaller triangle is 450 in²