Calculus

posted by .

A fence 2 feet tall runs parallel to a tall building at a distance of 6 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

  • Calculus -

    Let the ladder length be d
    Let the base of the ladder be x feet from the fence, and hit the wall at height h.

    from similar triangles,

    2/x = h/(6+x)
    h = 2(x+6)/x

    d^2 = (6+x)^2 + h^2
    = (x+6)^2 + 4(x+6)^2/x^2
    = (x+6)^2 * (1 + 4/x^2)

    d^2 (and therefore d) has a minimum at x = 2.9

    d^2 = 116.88
    d = 10.8 ft

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    A fence 5 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  2. Calculus

    A fence 6 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  3. Math: Calculus

    A fence 6 feet tall runs parallel to a tall building at a distance of 2 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  4. Calculus

    A fence 4 feet tall runs parallel to a tall building at a distance of 6 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  5. calculus

    A fence 5 feet tall runs parallel to a tall building at a distance of 3 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  6. calculus

    A fence 5 feet tall runs parallel to a tall building at a distance of 3 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  7. Calculus

    A fence 8 feet tall runs parallel to a tall building at a distance of 6 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  8. Calculus

    A fence 3 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  9. Calculus

    fence 3 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  10. Calculus

    A fence 4 feet tall runs parallel to a tall building at a distance of 2 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

More Similar Questions