Question

Corresponding sides of two similar triangles are in the ratio 2:3. If the area of the Smaller triangle is $48c{m^2}$ , to determine the area of the larger triangle.

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Hint: To solve this question we have to apply the property of similar triangles that “if two triangles are similar, then the ratio of the area of the both triangles is proportional to the ratio of squares of their corresponding sides.”

$\dfrac{{{\text{area of smaller triangle}}}}{{{\text{area of larger triangle}}}} = {\left( {\dfrac{2}{3}} \right)^2} \\ \\$
$\dfrac{{48}}{{{\text{area of larger triangle}}}} = \dfrac{4}{9} \\ \therefore {\text{area of larger triangle = }}\dfrac{{48 \times 9}}{4} = 108c{m^2} \\$
Hence the area of the larger triangle is $108c{m^2}$ .