In the adjoining figure, $D E ∥ B C .$ If $A D = x, D B = x - 2, A E = x + 2$ and $E C = x - 1$ . Find the value of $x$ .

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Solution

From basic proportionality theorem in the triangle,

$\frac{A D}{D B} = \frac{A E}{E C} ⟹ \frac{x}{x - 2} = \frac{x + 2}{x - 1} ⟹ x^{2} - x = x^{2} - 4 ⟹ x = 4$
The sides are $A D = 4$ , $D B = 2$ , $A E = 6$ and $E C = 3$ .

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