Question

IF $\Delta ABC\sim \Delta QRPar\left(\Delta ABC\right):ar\left(\Delta PQR\right)$ = 9:4, AB = 18 cm and BC = 15 cm, then find the length of QR.

Answer 1

As in similar triangles, ratio of areas is square of

ratio of sides,

$\Rightarrow$ if $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}=R\Rightarrow \frac{ar\left(\Delta ABC\right)}{ar\left(\Delta QRP\right)}=R^2$

Given $R^2=9/4\Rightarrow R=3/2\Rightarrow \frac{BC}{QR}=\frac{3}{2}\Rightarrow QR=\frac{2}{3}\times 15$

$\Rightarrow QR=10cm$