Question

How do I find X for this problem? I’m stuck

Answer 1

Corresponding sides of the two triangles occur in a ratio with one another. In particular, you have the relationship

$\dfrac6{6+x}=\dfrac{10}{15}=\dfrac y{y+4}$

We only need the first two parts to solve for $x$:

$\dfrac6{6+x}=\dfrac{10}{15}\implies6\cdot15=10(6+x)\implies90=60+10x\implies30=10x$

$\implies\boxed{x=3}$