Question

$\text{In the given figure,}AX:XB=3:5\text{and}XY||BC.$

$\text{If XY = 18 cm, then BC = \_\_\_ .}$

Answer 1

$\text{We are given that in the}\Delta ABC,AX:XB=3:5\text{and}XY||BC.$

$\Rightarrow \frac{XB}{AX}=\frac{5}{3}$

$\Rightarrow \frac{XB}{AX}+1=\frac{5}{3}+1$

$\Rightarrow \frac{XB+AX}{AX}=\frac{5+3}{3}$

$\Rightarrow \frac{AB}{AX}=\frac{8}{3}$

$\Rightarrow \frac{AX}{AB}=\frac{3}{8}$

$\text{Now in}\Delta AXY\text{and}\Delta ABC,$

$\angle AXY=\angle ABC\text{(Corresponding angles)}$

$\angle XAY=\angle BAC\text{(Common in both triangles)}$

$\therefore \Delta AXY\sim \Delta ABC\text{(By AA similarity criterion)}$

$\Rightarrow \frac{AX}{AB}=\frac{XY}{BC}$

$\Rightarrow \frac{3}{8}=\frac{18}{BC}$

$\therefore BC=\frac{18\times 8}{3}=48cm$