If a line intersects sides AB and AC of a $△ A B C$ at D and E respectively and is parallel to BC, then $\frac{A D}{A B}$ = $\frac{A E}{x}$ .Then $x$ is
___.

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Solution

DE $∥$ BC

So, $\frac{A D}{D B}$ = $\frac{A E}{E C}$

Or, $\frac{D B}{A D}$ = $\frac{E C}{A E}$

Adding 1 on both sides:

We get, $\frac{A B}{A D}$ = $\frac{A C}{A E}$ .

Hence, $\frac{A D}{A B}$ = $\frac{A E}{A C}$ .

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