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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Solution

We are given two triangles ABC and PQR such that $△$ ABC ~ $△$ PQR

Given AM = PO = 5 cm

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

Take the square root on both sides

Then, $\frac{5}{5 + O N}$ = $\frac{3}{5}$

25 = 15 + 3ON

ON = $\frac{10}{3}$

3ON = 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.

Δ A B C

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Δ A B C

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Δ P Q R

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Δ A B C

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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 $3 O N$ .

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

Δ A B C

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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.

We are given two triangles ABC and PQR such that △ABC ~ △PQR Given AM = PO = 5 cm So, area of △ ABCarea of △ PQR = AM2PN2 = 52(5+ON)2 = 925 Take the square root on both sides Then, 55+ON = 35 25 = 15 + 3ON ON = 103 3ON = 10 cm.

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.