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March 30, 2017

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One side of a triangle is x inches longer than another side. The ray bisecting the angle formed by these sides divides the opposite side into 3-inch and 5-inch segments. Find the perimeter of the triangle in terms of x. ( triangle angle bisector theorem)

  • Geometry - ,

    let the shorter side be a, then the longer side is a+x
    by the Triangle Angle Bisector Theorm

    (a+x)/5 = a/3
    3a + 3x = 5a
    3x = 2a
    a = 3x/2 = 1.5x

    so the sum of the three sides
    = a + a+x + 8
    = 1.5x + x + 8
    = 2.5x + 8

  • Geometry - ,

    Reiny, if a+a+x+8 then how come it is 1.5x+x+8=2.5x+8? I thought that it is 1.5x+1.5x+x+8=4x+8. Previous problem:one side of a triangle is x inches longer than another side. The ray bisecting the angle formed by these sides divides the opposite side into 3-inch and 5-inch segments. Find the perimeter of the triangle in terms of x.

  • Geometry - ,

    Anonymous is correct, for the answer is 4x+8.

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