Question

Which length of AC proves that AABC ~ ADEF? 40 16 72.7 9.4

Answer 1

To find the length of AC, we must form a proportional relation between the triangles. Observe that EF corresponds to BC, and DE corresponds to AB.

$\frac{EF}{BC}=\frac{DE}{AB}$

Replacing all the given expressions, we have.

$\frac{2x+10}{12}=\frac{56}{16}$

Now, we solve for x.

$\begin{gathered} 2x+10=56\cdot\frac{12}{16} \\ 2x+10=42 \\ 2x=42-10 \\ 2x=32 \\ x=\frac{32}{2} \\ x=16 \end{gathered}$

Then, we use this value to find AC.

$AC=2x+8=2(16)+8=32+8=40$

Therefore, AC must be 40 units long to prove that the triangles are similar.