What values of x will make DE $∥$ AB in the given figure?

Open in App

Solution

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

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

$\frac{3 x + 19}{x + 3} = \frac{3 x + 4}{x}$

$3 x^{2} + 19 x = 3 x^{2} + 4 x + 9 x + 12$

$19 x = 13 x + 12$

$6 x = 12$

$x = \frac{12}{6}$

Hence $x = 2$

Suggest Corrections

Similar questions

x

D E ∥ A B

?

x

D E ∥ A B

A D = 8 x + 9

C D = x + 3

B E = 3 x + 4

C E = x

Join BYJU'S Learning Program