Math

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Application of Quadratic Equations

The base of a triangle is longer than twice its corresponding height by 1 cm. The area of the triangle is 105 cm(square). Find the height of the triangle

  • Math -

    height ---- x
    base ---- 2x + 1

    (1/2)(base)(height) = area
    (1/2)(2x+1)(x) = 105
    x(2x+1) = 210
    2x^2 + x - 210 = 0
    (x-10)(2x+21) = 0
    x = 10 or x = -21/2 , but obviously x has to be positive, so

    x = 10
    The height is 10 cm

    check:
    height is 10
    base is 21
    area = (1/2)(21)(10) = 105
    answer is correct

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