Question

Points B, D, and F are midpoints of the sides of ΔACE. EC = 38 and DF = 16. Find AC. The diagram is not to scale.

Answer 1

Answer: The measure of AC is 32.

Explanation:

It is given that the Points B, D, and F are midpoints of the sides of ΔACE. EC = 38 and DF = 16.

The midpoint theorem states that the if a line segments connecting two midpoints then the line is parallel to the third side and it's length is half of the third side.

Since F and D are midpoints of AE and EC respectively.

So by midpoint theorem length of AC is twice of DF.

$AC=2\times DF$

$AC=2\times 16$

$AC=32$

Therefore, the length of AC is 32.