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.

`(EF)/(BC)=(DE)/(AB)`

Replacing all the given expressions, we have.

`(2x+10)/(12)=(56)/(16)`

Now, we solve for x.

`\begin{gathered} 2x+10=56\cdot(12)/(16) \\ 2x+10=42 \\ 2x=42-10 \\ 2x=32 \\ x=(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.