Question

I need to solve for x. I'm so confused with the whole 'Slide splitting theorem' thing ​

Answer 1

Triangles JFE and JLK are similar provided that line segments FE and LK are parallel. This means that corresponding parts of these triangles occur proportionally to one another. In particular,

`(JF)/(JL)=(JE)/(JK)=(FE)/(LK)`

From this relation we get

`(JF)/(JL)=(JE)/(JK)\implies((3x+21)-12)/(12)=(56)/(70)`

Now we can solve for
`x`:

`(3x+9)/(12)=\frac45`

`3x+9=12\cdot\frac45=\frac{48}5`

`3x=\frac{48}5-9=\frac35`

`x=\frac{\frac35}3=\frac15`