The corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm 2 , find the area of the larger triangle.

Question

Philoid · Accepted Answer

Let the smaller triangle be ABC and larger triangle beDEF.

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

i.e. ar(ABC)/ar(DEF) = (AB/DE)²

Substituting the given values, we get

⇒ 48cm²/ ar(DEF) = (2/3)²

⇒ 48cm²/ ar(DEF) = 4/9

⇒ ar(DEF)= (48 × 9)/4 cm²

⇒ ar(DEF) = 108cm²

108cm²

The corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm2, find the area of the larger triangle.

The corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm², find the area of the larger triangle.