maths

posted by Dd

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?

  1. Reiny

    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

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