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

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

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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.

5x+7=3x+16

2x=9

x=4.5

BF=5x+7

BF=[5(4.5)]+7

BF=22.5+7=29.5

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.