Question

The perimeters of two equilateral triangles are in the ratio 9:1 what is the ratio of their areas?

Answer 1

The ratio of their area is 81 : 1.

Explanation:

Given,

The perimeter of two equilateral triangles is 9:1

To find the ratio of their areas.

Formula

If each side of a equilateral triangle is a then perimeter = 3a and area =
`(√(3) )/(4)`a²

Now,

Perimeter of the 1st triangle is 9x

So, each side will be 3x

Again,

Perimeter of the 2nd triangle is x

So, each side will be
`(x)/(3)`

Now,

Area of the 1st triangle =
`(√(3) )/(4)`(3x)²

Area of the 2nd triangle =
`(√(3) )/(4)`(
`(x)/(3)`)²

Hence,

The ratio of their area =
`(√(3) )/(4)`(3x)² :

= 9x² :
`(x^(2) )/(9)`

= 81 : 1

Thus the obtained ration of the triangle is 81:1