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BF and FD are perpendicular bisectors of triangle ACE. Find the measure of segment BF if BF = 5x + 7 and FD = 3x + 16.

I do not know how to solve for the sides in an isosceles triangle with perpendicular bisectors. All help will be greatly appreciated 
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2 Answers

Hi Arlene;
As you probably already know, an isosceles triangle is a triangle in which two sides are equal.  Perpendicular bisectors BF and FD share the point F.  To resolve this with the information given, I must assume that F is on the non-equal side, and B is on one equal side, whereas D is on the other equal side.  If this is true, then BF=BD.
Please let me know if you have any additional information.
If you have an isosceles triangle, then the perpendicular bisectors which bisect the two equal sides will meet at a point called the circumcenter. Is this F? Then the  two segments will be equal, and you should set the two equations equal to each other.