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

Which length of AC proves that AABC ~ ADEF? 40 16 72.7 9.4-example-1

1 Answer

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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.

User Pham Trung
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