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Question is in image  Expert Answer
As ΔABC and ΔABF are similar.
And, AB is common between the two.
Hence, they are congruent triangles. Their area is same.

As D is the midpoint of AB, FD is the median from F in ΔABF.
Hence, FA = BC,   FB = AC = AB.

Using the formula for a median in a triangle (ABF)
4 FD² = 2 FB² + 2 FA² - AB²
= 2 AB² + 2 BC² - AB²
= AB² + 2 BC²

FD = 1/2 * √[AB²+2BC²]
Since DE is a line joining the midpoints of sides, DE = 1/2  BC.

Hence,  FE = FD - DE = 1/2 [ √(AB²+2BC²)  - BC ]
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