# Geometry

Christian lives directly east of the park the football field is directly south of the park the library sits on the line phone between Kristen’s home and the football field at that exact point where in altitude to the right triangle formed by her home the park and the football field could be drawn the library is 2 miles away from her home the football field is 5 miles away from the library . How far is the library from the park? How far is the Park from the football field?

1. 4
1. As always, draw a diagram. If we label the locations with the obvious letters (P,H,F,L) then we have

∆FPH ~ ∆FLP ~ ∆PLH

We want LP and PF. Using similar triangles,

5/PF = PF/7
PF² = 35

LP²+FL² = PF²
LP² + 25 = 35
LP² = 10

posted by Steve

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