Question

In the adjoining figure, $DE\parallel BC.$ If $AD=x,DB=x-2,AE=x+2$ and $EC=x-1$. Find the value of $x$.

Answer 1

From basic proportionality theorem in the triangle,

$\frac{AD}{DB}=\frac{AE}{EC}⟹\frac{x}{x-2}=\frac{x+2}{x-1}⟹x^2-x=x^2-4⟹x=4$

The sides are $AD=4$,$DB=2$,$AE=6$ and $EC=3$.