maths

posted by .

two poles 6m and 15m tall are 20 m apart a wire is attached to the top of each pole and is also staked to the ground some where b/n two poles where should be the wire be staked so that the minimum amount of wire be used?

  • maths -

    make a sketch.
    draw poles AB and PQ with B and Q on the ground
    Draw the reflection of AB in the horizontal and call it BA'. Joint A' to P
    Label the intersection of A'P with BQ as M.
    let BM = x, then
    MQ = 20-x

    Of course the shortest distance between any two points is the straight line joining them, So A'P is the shortest
    but A'P = AM + MP <--- the shortest

    since triangles ABM and PQM are similar,
    AB/BM = PQ/MQ
    6/x = 15/(20-x)
    15x = 120 - 6x
    21x = 120
    x = 120/21 = 40/7

    Attach it 40/7 m from B

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. geometry

    A guy wire is used to stabilize a utility pole. The wire is fastened to the pole 25 feet above the ground, and staked into the ground 4 feet from the base of the pole. (No stand-offs are used, the wire goes directly from the pole to …
  2. Physics

    A bird is resting on a phone wire between two poles that are 30 m apart. The bird is exactly midway between the two poles. Because of the weight of the bird, the wire sags by 50 cm. The tension in the wire is 70 N
  3. Algebra

    A wire is run between two tips of two poles. One pole is 23 ft. taller than the other pole. The poles are 37 ft. apart. How long does the wire need to be to reach between the two poles?
  4. geometry

    Two poles, 60 feet tall and 20 feet tall, stand on opposite sides of a field. The poles are 80 feet apart. Support cables are placed from the top of each pole to the bottom of the opposite pole. How far above the ground is the intersection …
  5. Math

    A guy wire is attached to the top of a pole. The other end of the guy wire is staked in the ground 29 feet from the base of the pole. How tall is the pole, if the guy wire is 73 feet long?
  6. math (algebra)

    An auto dealer wants to string a wire from the top of a pole to the ground and hang colorful pennants from it. The distance from the base of the pole to the point where the wire is attached to the ground is 3 times the height of the …
  7. algebra

    Two vertical poles 20m and 30m high are 60m apart.A rope is to be attached from the top of one pole to a point on the ground halfway between the poles and then to the top of the other pole.How long a rope is needed?
  8. Math

    Two telephone poles are 60ft. apart, and one of them is 6ft. higher than the other. If the length of the wire between the poles is 61.3 ft., how much wire was allowed for sag?
  9. Geometry

    Two telephone poles are 60ft. apart, and one of them is 6ft. higher than the other. If the length of the wire between the poles is 61.3 ft., how much wire was allowed for sag?
  10. Maths

    A 5 metre tall vertical pole is supported by a guy wire. The wire is attached to the top of the pole and is attached to the ground 3 metres from the base of the pole

More Similar Questions