Question

In the given figure, find the value of x which will make DE || AB ?

Answer 1

If $DE||AB$, then $\Delta CDE\sim \Delta ABC$
By property of similar triangles:
$\frac{CD}{AC}=\frac{CE}{BC}$
$⟹\frac{x+3}{4x+22}=\frac{x}{4x+4}$
Cross-multiplying:
$(x+3)(4x+4)=x(4x+22)$
$⟹4x^2+16x+12=4x^2+22x$
$12=6x⟹x=2$