Question

I'm pretty sure I'm doing this wrong. A little help? Thanks in advance.

Answer 1

I believe by "redraw" you are expected to separate the given triangle into the 3 similar-triangle components. You've almost done this correctly - the leftmost triangle should have its hypotenuse labeled $z$.

Then use the similarity between them to establish an appropriate equation. For example, the first triangle contains the three triangles RST, SPT, and RPS. Because these triangles are similar, we have the relationship

$\dfrac{RS}{RT}=\dfrac{RP}{RS}\iff\dfrac z{24+6}=\dfrac6z$

$\implies z^2=6(24+6)=180\implies z=6\sqrt5$

In the second triangle, we have

$\dfrac x6=\dfrac64\implies x=\dfrac14$

Question 3 uses the same setup as question 1, so you should get $x=2\sqrt7$.