Question : 360 cm2 and 250 cm2 are the areas of the two similar triangles. If the length of one of the sides of the first triangle is 8 cm, then the length of the corresponding side of the second triangle is:
Option 1: $6\frac{1}{5}\;\operatorname{ cm}$
Option 2: $6\frac{1}{3}\;\operatorname{ cm}$
Option 3: $6\frac{2}{3}\;\operatorname{ cm}$
Option 4: $6\;\operatorname{ cm}$
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Correct Answer: $6\frac{2}{3}\;\operatorname{ cm}$
Solution : Thales theorem states that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Let the length of the corresponding side of the second triangle as $x$. $⇒\mathrm{\frac{Area_1}{Area_2} = \left(\frac{Side_1}{Side_2}\right)^2}$ $⇒\frac{360}{250} = \left(\frac{8}{x}\right)^2$ $⇒\frac{6}{5} = \left(\frac{8}{x}\right)$ $⇒x=\frac{20}{3}$ $⇒x=6\frac{2}{3}\;\operatorname{ cm}$ Hence, the correct answer is $6\frac{2}{3}\;\operatorname{ cm}$.
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