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

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

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Answer : [108 cm2]

Given:- Corresponding sides of two similar triangles are in the ratio of 2 : 3.

Area of smaller triangle = 48 cm2

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

i.e \frac{ar\left ( \text {smaller triangle} \right )}{ar\left ( \text {larger triangle} \right )}=\left ( \frac{2}{3} \right )^{2}

\frac{48}{ar\left ( \text {larger triangle} \right )}=\frac{4}{9}

ar\left ( \text {larger triangle} \right )=\frac{48 \times 9}{4}=12 \times 9=108\; cm^{2}

Posted by

infoexpert23

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