Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’s home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 4 miles from her home. The football field is 10 miles from the library.

Question

Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’s home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 4 miles from her home. The football field is 10 miles from the library.
How far is the library from the park?
How far is the park from the football field
A. 7 miles and 12 miles
B.2 square root of 10 and 2 square root of 6
C.square root of 14 and 2 square root of 6
D. 2 square root of 10 and 2 square root of 35

Steve · Answer

Label the various points P,K,F,L using similar triangles, PL/4 = 10/PL PL=2√10 10/PF=PF/14 PF=2√35