algebra

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A triangle has sides of lengths 20, 28, and 32. A similiar triangle has a side of length 15 and another of length 24. How long is the third side of this triangle?

  • algebra -

    for similar triangles, the ratio of the sides of the first triangle is equal to the ration of the corresponding sides of the second triangle,, like:
    let h1 = height of 1st triangle
    let h2 = height of 2nd triangle
    let b1 = base of 1st triangle
    let b2 = base of 2nd triangle
    therefore, if they are similar triangles,
    (h1)/(b1) = (h2)/(b2)

    thus in the question, we can write:
    let x = third side
    20/15 = 32/24 = 28/x
    simplifying:
    4/3 = 28/x
    solving for the third side,
    x = 21

    hope this helps~ :)

  • algebra -

    20/15 = 4/3

    28/24 = nope
    32/24 = 4/3 yes

    so
    20 --> 15
    32 --> 24
    28(3/4) = 21

    so
    20 , 28 , 32
    --->
    15 , 21 , 24

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