Question

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

Answer 1

We are given two triangles i.e. $\Delta$ABC and $\Delta$PQR such that $\Delta ABC\sim \Delta PQR$
Given AM = PO = 5 cm
So, $\frac{Areaof\Delta ABC}{Areaof\Delta PQR}=\frac{A{B}^2}{P{Q}^2}=\frac{9}{25}\Rightarrow \frac{AB}{PQ}=\frac{3}{5}Also\Delta ABM\sim \Delta PQNSo,\frac{AB}{PQ}=\frac{AM}{PN}=\frac{3}{5}\Rightarrow \frac{5}{5+ON}=\frac{3}{5}Then25=15+3\left(ON\right)ON=\frac{10}{3}3\left(ON\right)=10cm\text{Hence the length of 3(ON) is 10 cm.}$