In the given figure, $D E ∥ A C$ . Find the value of x.

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Solution

In $△ A B C$ ,

$D E ∥ A C$

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

$\frac{2 x + 10}{3 x} = \frac{x + 7}{2 x}$

$2 x (2 x + 10) = 3 x (x + 7)$

$4 x^{2} + 20 x = 3 x^{2} + 21 x$

$x^{2} - x = 0$

$x (x - 1) = 0$

$x - 1 = 0$

$x = 1$

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