ABC and PQR are two similar triangles as shown in the figure such that Area of ABC -9-25- AM and PN are the medians on ABC and PQR respectively- If AM - PO -5 cm- find the value of 3 ON-

We are given two triangles ABC and PQR such that ABC PQR Given AM = PO = 5 cm So, area of ABC/ area of PQR = AM^2/PN^2 = 5^2/(5+ON)^2 = 9/25 [Ratio of ...

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Standard X

Mathematics

Ratio of Area of Similar Triangles

ABC and PQR a...

Question

$△$ 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.

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Solution

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

Given AM = PO = 5 cm

So, $\frac{a r e a o f △ A B C}{a r e a o f △ P Q R}$ = $\frac{A M^{2}}{P N^{2}}$ = $\frac{5^{2}}{(5 + O N)^{2}}$ = $\frac{9}{25}$ [Ratio of areas of two similar triangles is equal to the ratio of the squares of their median]

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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△ABC and △PQR are two similar triangles as shown in the figure such that Area of ABCArea of PQR = 925. AM and PN are the medians on △ABC and △PQR respectively. If AM = PO = 5 cm, find the value of 3ON. __

$△$ 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.

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