Question

In the adjoining figure,D is a point on BC such that $\angle$$ABD=$$\angle$$CAD$. If $AB=5cm,AD=4cm$ and $AC=3cm.$.Find $BC$

Answer 1

In $△$ ABC and $△$ CAD
$\angle ABD=\angle CAD$ (Given)
$\angle ACB=\angle ACD$ (Common angle)
$\angle CAB=\angle CDA$ (Third angle)
Hence, $△ABC\sim △DAC$ (AAA rule)
$\frac{AB}{AD}=\frac{BC}{AC}$ (Ratio of corresponding sides of similar triangles is equal)
$\frac{5}{4}=\frac{BC}{3}$
$BC=3.75cm$