Question

. Triangle ACE below is an isosceles triangle with legs AC and CE. BF and FD are perpendicular bisectors of triangle ACE. Find the measure of segment BF if BF = 5x + 7 and FD = 3x + 16.

Answer 1

Due to symmetry, BF=FD. That means\[BF = 5x + 7 =FD = 3x + 16 \implies 2x=9 \implies x=\frac{9}{2} \implies BF=\frac{59}{2}\]

Answer 2

Hope that was clear enough. Do math every day.