Question

How do you find the missing side??

Answer 1

The answer is 12 if I’m not mistaken

Answer 2

Answer:

$\boxed{\ell = 12}.$

Step-by-step explanation:

Let $\ell$ denote the length of the missing side. Since $\triangle ABC$ and $\triangle AXY$ share one vertex and $\overline{XY}\parallel \overline{BC}$, these triangles are similar. This means that:

$\dfrac{AX}{AB} = \dfrac{AY}{AC} \iff \dfrac{\ell}{18+\ell} = \dfrac{14}{14+21} \iff\dfrac{\ell}{18+\ell} = \dfrac{14}{35}.$

We now multiply both sides by $18+\ell$ and solve the equation:

$\dfrac{\ell}{18+\ell} = \dfrac{14}{35} \iff \ell = \dfrac{36}{5} + \dfrac{14}{35}\ell \iff \ell \left(1-\dfrac{14}{35}\right) = \dfrac{36}{5} \iff \dfrac{3}{5}\ell = \dfrac{36}{5}.$

So we now simply get:

$\boxed{\ell = \dfrac{36}{3} = 12}.$