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.
ANSWER
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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.”
Complete step-by-step answer: We know If two triangles are similar then the ratio of area of the both triangles is proportional to the ratio of square of their corresponding sides. Hence we can write, $ \dfrac{{{\text{area of smaller triangle}}}}{{{\text{area of larger triangle}}}} = {\left( {\dfrac{2}{3}} \right)^2} \\ \\ $ Now using the data given in question, we get
$ \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 $108c{m^2}$ .
Note: Whenever we get this type of question the key concept of solving is that if no more data is given in question then we should understand that it must be any property from which it can be easily solved so we have to think in this type of question that which property is perfect for this question.