The corresponding sides of two similar triangles are in the ratio 2:3,

1.	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.
Answer» We know that the ratio of area of two similar triangle is the square of the ratio of corresponding sides of these similar triangles. Let the area of the larger triangle is A cm² . Given that the area of the smaller triangle is 48 cm² and their corresponding sides are in the ratio 2 : 3. Therefore, \(\frac{48}{A} = (\frac{2}{3})^2\) (The ratio of Area of similar triangles is the square of the ratio of their corresponding sides.) ⇒ A = 48 × \((\frac{3}{2})^2\) ⇒ A = 48 × \(\frac{9}{4}\) = 12 × 9 = 108. Hence, the area of the larger triangle is 108 cm².

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.

Answer»

We know that the ratio of area of two similar triangle is the square of the ratio of corresponding sides of these similar triangles.

Let the area of the larger triangle is A cm² .

Given that the area of the smaller triangle is 48 cm² and their corresponding sides are in the ratio 2 : 3.

Therefore, \(\frac{48}{A} = (\frac{2}{3})^2\) (The ratio of Area of similar triangles is the square of the ratio of their corresponding sides.)

⇒ A = 48 × \((\frac{3}{2})^2\)

⇒ A = 48 × \(\frac{9}{4}\) = 12 × 9 = 108.

Hence, the area of the larger triangle is 108 cm².

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