calculus

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the base of a triangle is 2 cm shorter than the width of a rectangle. The rectangle's length is 4 times its width and the triangle's height is the same as the rectangle's length. find the area of both figures if the difference of the two areas is 30cm2

  • calculus -

    from the data
    rectangle:
    width = x
    length = 4x

    triangle:
    base = x-2
    height = 4x

    area of rectangle = x(4x) = 4x^2
    area of triangle = (1/2)(x-2)(4x) = 2x^2 - 4x

    given:
    4x^2 - (2x^2 - 4x) = 30
    2x^2 + 4x - 30 = 0
    x^2 + 2x - 15=0
    (x+5)(x-3) = 0
    x = -5 (not possible) or x = 3

    area of rect. = 4x^2 = 36
    area of triangle = 2x^2 - 4x = 18-16 = 2

  • Oops - calculus -

    I messed up in the last line

    should have said:
    area of triangle = 2x^2 - 4x = 18-12 = 6

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