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,

`(x-6)/((x-6)+3)=\frac x{x+5}`

Solve for
`x`:

`(x-6)/(x-3)=\frac x{x+5}`

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

`x^2-x-30=x^2-3x`

`2x=30`

`\boxed{x=15}`