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10 November, 18:55

Solve with the Quadratic Formula:

The length of a rectangle is 1 less than 2 times the width. The area of the rectangle is 45 cm^2. Find the length and width.

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  1. 10 November, 19:58
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    Let the width be x.

    Length = 2x - 1

    The area of rectangle = 45 cm²

    x * (2x - 1) = 45

    2x² - x = 45

    2x² - x - 45 = 0 This is a quadratic equation

    comparing to ax² + bx + c = 0, a = 2, b = - 1, c = - 45

    x = (-b + √ (b² - 4ac)) / 2a or (-b - √ (b² - 4ac)) / 2a

    x = ( - - 1 + √ ((-1) ² - 4*2*-45)) / 2*2 or ( - - 1 - √ ((-1) ² - 4*2*-45)) / 2*2

    x = (1 + √ (1 + 360)) / 2*2 or (1 - √ (1 + 360) / 2*2

    x = (1 + √361) / 4 or (1 - √361) / 4

    x = (1 + 19) / 4 or (1 - 19) / 4

    x = 20/4 or - 18/4

    x = 5 or - 4.5

    x can't be negative since we are solving for side.

    x = 5 as the only valid solution.

    Recall, the width = x = 5.

    Length = 2x - 1 = 2*5 - 1 = 10 - 1 = 9

    Hence the length = 9cm, and width = 5cm
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