Question

What is the value of x? Please help!

Answer 1

Triangles KPQ and KJL are similar because the line segments PQ and JL are parallel. This means corresponding parts of the triangles occur in the same ratio. In particular,

$\dfrac{x-6}{(x-6)+3}=\dfrac x{x+5}$

Solve for $x$:

$\dfrac{x-6}{x-3}=\dfrac x{x+5}$

$(x-6)(x+5)=x(x-3)$

$x^2-x-30=x^2-3x$

$2x=30$

$\boxed{x=15}$