The ratio of the corresponding altitudes of two similar triangles is $\frac{3}{5}$. Is it correct to say that the ratio of their areas is $\frac{6}{5}$? Why?
(B) The statement is False.
According to the theorem on the areas of similar triangles,the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding altitudes.
$\frac{\text{Area}_1}{\text{Area}_2} = \left( \frac{\text{Altitude}_1}{\text{Altitude}_2} \right)^2$
Given that the ratio of the altitudes is $\frac{3}{5}$,we have:
$\frac{\text{Area}_1}{\text{Area}_2} = \left( \frac{3}{5} \right)^2 = \frac{9}{25}$
Since $\frac{9}{25} \neq \frac{6}{5}$,the given statement is incorrect.
According to the theorem on the areas of similar triangles,the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding altitudes.
$\frac{\text{Area}_1}{\text{Area}_2} = \left( \frac{\text{Altitude}_1}{\text{Altitude}_2} \right)^2$
Given that the ratio of the altitudes is $\frac{3}{5}$,we have:
$\frac{\text{Area}_1}{\text{Area}_2} = \left( \frac{3}{5} \right)^2 = \frac{9}{25}$
Since $\frac{9}{25} \neq \frac{6}{5}$,the given statement is incorrect.
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