The perimeters of two similar triangles are 36 cm and 24 cm, respectively. Find the ratio of their areas.

GIVEN:

The perimeters of two similar triangles are 36 cm and 24 cm respectively

FORMULA USED:

If we have two  similar triangles, say ABC and DEF

Ar(\(\triangle\) ABC)/Ar(\(\triangle\)DEF) = (Perimeter of \(\triangle\) ABC/Perimeter of \(\triangle\) DEF)²

CALCULATION:

Here, the perimeters of two similar triangles are 36 cm and 24 cm respectively

Let us say Area of the first and second similar triangles be A₁ and A₂ respectively 

And their perimeters be P₁ and P₂ respectively 

As we know that 

⇒  (Area)₁/(Area)₂ = [(Perimeter)₁/(Perimeter₂)]²

⇒ (Area)₁/(Area)₂ = (36/24)² = 1296/576  = 9/4

⇒ (Area)₁ : (Area)₂ = 9 : 4 

Hence, the ratio of their areas is 9 : 4.