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  • The areas of two similar triangles are 81 cm2 and 49 cm2 respectively. If the altitude of the bigger triangle is 9 cm, find the corresponding altitude of the smaller triangle.

The areas of two similar triangles are 81 cm2 and 49 cm2 respectively. If the altitude of the bigger triangle is 9 cm, find the corresponding altitude of the smaller triangle.

Option: 1

3.5 cm


Option: 2

4.5 cm


Option: 3

6 cm


Option: 4

7 cm


Answers (1)

best_answer

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

Let two similar triangles be ABC and DEF

\\ \therefore \quad \frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\Delta D E F)}=\frac{A L^{2}}{D M^{2}} \\ \\\Rightarrow \quad\left(\frac{A L}{D M}\right)^{2}=\frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\triangle D E F)}=\frac{81}{49}=\left(\frac{9}{7}\right)^{2} \\ \\\Rightarrow \quad \frac{A L}{D M}=\frac{9}{7} \Rightarrow \frac{9}{D M}=\frac{9}{7} \\ \\\Rightarrow \quad D M=\frac{9 \times 7}{9} cm =7 cm

Posted by

seema garhwal

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