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  • 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?

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

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Answer: [False]

Given:- Ratio of corresponding altitudes of two similar triangles is 3/5

As we know that the ratio of the areas of two similar triangles is equal to the ratio of squares of any two corresponding altitudes.

\therefore \frac{\text {Area 1}}{\text {Area 2}}=\left ( \frac{\text {Altitude 1}}{\text {Altitude 2}} \right )^{2}

\frac{\text {Area 1}}{\text {Area 2}}=\left ( \frac{3}{5} \right )^{2}            \left [ Q\frac{\text {Altitude 1}}{\text {Altitude 2}}=\frac{3}{5} \right ]

=\frac{9}{25}

Hence the given statement is false because ratio of areas of two triangles is 9/25 which is not equal to 6/5

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infoexpert23

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