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,

$\dfrac{JF}{JL}=\dfrac{JE}{JK}=\dfrac{FE}{LK}$

From this relation we get

$\dfrac{JF}{JL}=\dfrac{JE}{JK}\implies\dfrac{(3x+21)-12}{12}=\dfrac{56}{70}$

Now we can solve for $x$:

$\dfrac{3x+9}{12}=\dfrac45$

$3x+9=12\cdot\dfrac45=\dfrac{48}5$

$3x=\dfrac{48}5-9=\dfrac35$

$x=\dfrac{\frac35}3=\dfrac15$