Math

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the right triangle ABC, the altitude from vertex C divides the hypotenuse into two segments, one of length 2 and the other of length 16. Find the perimeter of triangle ABC.

  • Math -

    C must be the right angle.
    You have 3 similar triangle, the original and 2 smaller ones
    let the altitude be h
    2/h = h/16
    h^2 = 32
    h = √32

    in the smaller right-angled triangle
    h^2 + 2^2 = BC^2
    BC^2 = 32 + 4 = 36
    BC = 6
    In the other right-angled triangle:
    AC^2 = h^2 + 16^2
    = 32 + 256 = 288
    AC = √288 = 12√2

    perimeter of ABC = 6 + 12√2 + 18
    = 24 + 12√2

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