The ratio of the corresponding altitudes of two similar triangles is $ \frac{3}{5} $. Is it correct to say that ratio of their areas is $ \frac{6}{5} $ ? Why?

Given:

The ratio of the corresponding altitudes of two similar triangles is \( \frac{3}{5} \). 

To do:

We have to find whether the ratio of their areas is \( \frac{6}{5} \).

Solution:

We know that,

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. Therefore,

$\frac{\text { Area of 1st triangle }}{\text { Area of 2nd triangle }}=(\frac{\text { Altitude of 1st triangle }}{\text { Altitude of 2nd triangle }})^2$

$=(\frac{3}{5})^2$

$=\frac{9}{25}$

Therefore, 

The ratio of the areas of the given triangles is  not equal to \( \frac{6}{5} \).

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Updated on: 10-Oct-2022

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