In the diagram below, start overline, E, F, end overline
EF
is parallel to start overline, B, C, end overline
BC
. If E, FEF is 22 more than B, EBE, E, D, equals, 16ED=16, and B, C, equals, 15BC=15, find the length of start overline, B, E, end overline
BE
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Based on the given information, we can set up the following relationships:
EF = BC (parallel lines)
EF = BE + BC (triangle EFBC)
BE + BC + 22 = 16 (EF is 22 more than BE, and EF is 16)
Substituting BC for EF in the second equation, we get:
BE + BE + BC + 22 = 16
2BE + BC + 22 = 16
Substituting 15 for BC, we get:
2BE + 15 + 22 = 16
2BE + 37 = 16
Subtracting 37 from both sides, we get:
2BE = -21
Dividing both sides by 2, we get:
BE = -21/2
Therefore, the length of BE is -21/2, which cannot be simplified further.