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15 May, 09:26

The area of a rectangle is 20 square inches. If the length is 4 inches less than 6 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.

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  1. 15 May, 12:53
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    dimensions are 2.19 inches by 9.14 inches

    Step-by-step explanation:

    Here, we are interested in knowing the dimensions of the rectangle

    Now, let the width of the rectangle be x, from the question, we can write;

    6x-4 as the length

    Area of rectangle = l * b

    x (6x-4) = 20

    6x^2 - 4x = 20

    divide through by 2

    3x^2-2x = 10

    3x^2 - 2x - 10 = 0

    using quadratic formula;

    x = - b ± √ (b^2 - 4ac) / 2a

    From the quadratic equation, a = 3, b = - 2 and c = - 10

    substituting these values, we have

    x = 2 ± √ (-2) ^2 - 4 (3) (-10)) / 6

    x = 2 ± √ (124) / 6

    x = 2 + √ (124) / 6 or 2 - √ (124) / 6

    x = (2+11.14) / 6 or (2-11.14) / 6

    x = 2.19 or - 1.52

    Since width cannot be negative, we choose 2.19 alone

    So the length is 6 (2.19) - 4 = 9.14
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