Geometry

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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.
a. How far is library from the park?
b. How far is the park from the football field?

7 miles; 12 miles
2sqrt10 miles; 2sqrt6 miles
sqrt14 miles; 2sqrt6 miles
2sqrt10 miles; 2sqrt35 miles

  • Geometry -

    Draw a diagram where
    P = park
    K = Kristen's house
    F is the field
    L is the library

    a = PL
    b = PF
    h is the altitude, PL

    b/a = h/4
    a/b = h/10

    h/4 = 10/h
    h^2 = 40
    h = 2√10

    b^2 = h^2 + 10^2 = 40 + 100 = 140
    b = 2√35

    Choice (D)

  • Geometry -

    Oops a = PK

  • Geometry -

    tduktuk

  • Geometry -

    Thank you so much this was complicated

  • Geometry -

    this ballin hard

  • Geometry -

    Was this right?

  • Geometry -

    I think it is right but I'm not sure...

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