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- anonymous

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 9 miles from her home. The football field is 12 miles from the library.

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- anonymous

- chestercat

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- anonymous

- campbell_st

ok... you need to use the ratio of corresponding sides.... to start
looking at the original diagram
|dw:1435178035942:dw|
using the ratio of corresponding sides
\[\frac{x}{12} = \frac{9}{x}\]
cross multiply and you find x( the Library to park distance) is
\[x^2 = 108\]
you can simplfy this

- campbell_st

to find the 2nd part, the park to the football fields, use pythagoras
\[PF^2 = x^2 + 12^2\]
you know x^2 so
\[PF^2 = 108 + 144\]
you can simplify this as well.
hope it helps...

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