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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.

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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.

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