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  • The areas of two similar triangles are 144 cm2 and 64 cm2 respectively. If the median of fi rst triangle is 14.4 cm, find the corresponding median of the other.

The areas of two similar triangles are 144 cm2 and 64 cm2 respectively. If the median of fi rst triangle is 14.4 cm, find the corresponding median of the other.

Option: 1

9.6 cm


Option: 2

8.8 cm


Option: 3

9.2 cm


Option: 4

None of the above


Answers (1)

best_answer

The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding medians.

\large \begin{array}{l} \therefore \quad \frac{\operatorname{ar}(\Delta A B C)}{\operatorname{ar}(\Delta D E F)}=\frac{A P^{2}}{D Q^{2}} \\ \Rightarrow \quad\left(\frac{A P}{D Q}\right)^{2}=\frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\Delta D E F)}=\frac{144}{64}=\left(\frac{12}{8}\right)^{2} \\ \Rightarrow \frac{A P}{D Q}=\frac{12}{8} \Rightarrow \frac{14.4}{D Q}=\frac{12}{8} \end{array}

\Rightarrow D Q=\frac{(14.4 \times 8)}{12} cm =(1.2 \times 8) cm =9.6 cm

Posted by

himanshu.meshram

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