Question

I need help on how to do this exactly bescsue I have a test soon

Answer 1

Given

we are given a triangle

Here

$\angle1=\angle2$

and they are corresponding angles. so DE is parallel to BC.

$\Rightarrow\angle3=\angle4$

Now in triangles ADE and ABC

we have

$\begin{gathered} \angle1=\angle2 \\ \angle3=\angle4 \end{gathered}$

so by AA criteria the triangles are similar.

Now since triangles are similar their corresponding sides are proportional.

so

$\begin{gathered} \frac{AB}{AD}=\frac{AC}{AE}=\frac{BC}{DE} \\ \frac{x+3}{x}=\frac{17}{12}=\frac{y}{6} \\ \Rightarrow12x+36=17x\text{ and }y=\frac{17}{2} \\ x=\frac{36}{5}\text{ and }y=8.5 \\ x=7.2\text{ and }y=8.5 \end{gathered}$

which is the required answer.