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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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Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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.
Marie B. | Marie B. Math and Physics tutorMarie B. Math and Physics tutor
4.8 4.8 (249 lesson ratings) (249)
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.