AM and PN are the medians of two similar triangles- ABC and PQR respectively and Area of ABC - Area of PQR -9-25-If AM - PO -5 cm- find the value of 3 ON-A- 10 cmB- 12 cmC- 13 cmD- 9 cm

The correct option is A 10 cmWe are given two triangles ABC and PQR such that Area of ABC/Area of PQR nbsp;= 9/25. Given: AM = PO = 5 cm We know that rat ...

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Standard X

Mathematics

Ratio of Area of Similar Triangles

AM and PN are...

Question

AM and PN are the medians of two similar triangles, $△$ ABC and $△$ PQR respectively and $\frac{A r e a o f △ A B C}{A r e a o f △ P Q R}$ = $\frac{9}{25}$ .

If AM = PO = 5 cm, find the value of $3 O N$ .

10 cm

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12 cm

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13 cm

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9 cm

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Solution

The correct option is A 10 cm
We are given two triangles ABC and PQR such that $\frac{A r e a o f △ A B C}{A r e a o f △ P Q R}$ = $\frac{9}{25}$ .

Given: AM = PO = 5 cm

We know that ratio of areas of two similar triangles is equal to the ratio of the squares of their median.

So, $\frac{a r e a o f △ A B C}{a r e a o f △ P Q R}$ = $\frac{A M^{2}}{P N^{2}}$ = $\frac{5^{2}}{(5 + O N)^{2}}$ = $\frac{9}{25}$
$\Rightarrow \frac{5}{5 + O N}$ = $\frac{3}{5}$

$\Rightarrow 25 = 15 + 3 O N$

$\Rightarrow 3 O N$ = 10 cm

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Similar questions

$△$ ABC and $△$ PQR are two similar triangles as shown in the figure such that $\frac{A r e a o f A B C}{A r e a o f P Q R}$ = $\frac{9}{25}$ . AM and PN are the medians on $△$ ABC and $△$ PQR respectively. If AM = PO = 5 cm, find the value of 3ON.

If $△$ ABC and $△$ PQR are two similar triangles shown in the figure. AM and PN are the medians on $△$ ABC and $△$ PQR respectively. The ratio of areas of $△$ ABC and $△$ PQR is 9:25. If AM = PO = 5 cm. Find the value of 3ON.

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Δ A B C

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In the given figure, $△ A B C \sim △$ PQR and AM and PN are medians of $△$ ABC and $△$ PQR respectively. Find the value of $\frac{A r e a o f △ A B C}{A r e a o f △ P Q R}$ .

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AM and PN are the medians of two similar triangles, △ABC and △PQR respectively and Area of △ABCArea of △PQR = 925. If AM = PO = 5 cm, find the value of 3 ON.

AM and PN are the medians of two similar triangles, $△$ ABC and $△$ PQR respectively and $\frac{A r e a o f △ A B C}{A r e a o f △ P Q R}$ = $\frac{9}{25}$ .

If AM = PO = 5 cm, find the value of $3 O N$ .