Question : The sides of two similar triangles are in the ratio 5 : 7. The areas of these triangles are in the ratio of:
Option 1: 35 : 49
Option 2: 15 : 49
Option 3: 25 : 49
Option 4: 36 : 49
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Correct Answer: 25 : 49
Solution :
The sides of two similar triangles are in the ratio of 5 : 7.
Let the sides be $5x$ and $7x$.
In two similar triangles, the ratio of their areas is square of the ratio of their sides.
$\frac{\textnormal{Area of triangle 1}}{\textnormal{Area of triangle 2}}=\frac{(\textnormal{Side of triangle 1})^2}{(\textnormal{Side of triangle 2})^2}$
$⇒\frac{\textnormal{Area of triangle 1}}{\textnormal{Area of triangle 2}}=\frac{({5x})^2}{({7x})^2}$
$\therefore\frac{\textnormal{Area of triangle 1}}{\textnormal{Area of triangle 2}}=\frac{25}{49}$
Hence, the correct answer is 25 : 49.
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