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11 April, 02:47

A right triangle has a height 8 cm more than twice the length

of the base. If the area of the triangle 96 cm², what are the

dimensions of the triangle?.

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Answers (1)
  1. 11 April, 02:53
    0
    B = 8cm

    H = 24cm

    Step-by-step explanation:

    H = Height

    B = Base

    A = Area

    A = 1/2 * BH

    A height 8 cm more than twice the length

    of the base

    H = 8 + 2B

    The area of the triangle 96 cm²

    A = 96

    Substitute H in terms of B in the equation.

    96 = 1/2 * (8 + 2B) * B

    96 = 1/2 * (8B + 2B²)

    96 = 4B + B²

    Trial and error by finding all the squares below 96

    * B = 9, 36 + 81 = 107

    * B = 8, 32 + 64 = 98

    B = 8, put that into the H equation to find the height.

    H = 8 + 2B

    H = 8 + 16

    H = 24

    A = 1/2 * 8 * 24 = 96
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