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

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Solution

We are given two triangles i.e. $Δ$ ABC and $Δ$ PQR such that $Δ A B C \sim Δ P Q R$
Given AM = PO = 5 cm
So, $\frac{A r e a o f Δ A B C}{A r e a o f Δ P Q R} = \frac{A B^{2}}{P Q^{2}} = \frac{9}{25} \Rightarrow \frac{A B}{P Q} = \frac{3}{5} A l s o Δ A B M \sim Δ P Q N S o, \frac{A B}{P Q} = \frac{A M}{P N} = \frac{3}{5} \Rightarrow \frac{5}{5 + O N} = \frac{3}{5} T h e n 25 = 15 + 3 (O N) O N = \frac{10}{3} 3 (O N) = 10 c m Hence the length of 3(ON) is 10 cm.$

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