The length of a rectangle is 13 centimeters less than three times its width. Its area is 56 square centimeters. Find the dimensions of the r

Question

The length of a rectangle is 13 centimeters less than three times its width. Its area is 56 square centimeters. Find the dimensions of the rectangle. Use the​ formula, area=length*width.

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Nem 6 months 2021-07-19T08:45:57+00:00 2 Answers 4 views 0

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    0
    2021-07-19T08:47:10+00:00

    Answer:

    The dimensions of the rectangle are 8 by 7 centimeters.

    Step-by-step explanation:

    The length of a rectangle is 13 centimeters less than three times its width. In other words:

    \ell = 3w-13

    Given that the area of the rectangle is 56 square centimeters, we want to determine its dimensions.

    Recall that the area of a rectangle is given by:

    A = w \ell

    Substitute in known values and equations:

    (56)=w(3w-13)

    Solve for w. Distribute:

    3w^2-13w=56

    Isolate the equation:

    3w^2-13w-56=0

    Factor. We want to find two numbers that multiply to 3(-56) = -168 and that add to -13.

    -21 and 8 suffice. Hence:

    3w^2 - 21w + 8w - 56 = 0 \\ \\ 3w(w-7) + 8(w-7) = 0 \\ \\ (3w+8)(w-7) = 0

    Zero Product Property:

    3w+8=0\text{ or } w-7=0

    Solve for each case:

    \displaystyle w = -\frac{8}{3} \text{ or } w=7

    Since the width cannot be negative, we can ignore the first solution.

    Therefore, the width of the rectangle is seven centimeters.

    Thus, the length will be:

    \ell = 3(7) - 13 = 8

    Thus, the dimensions of the rectangle are 8 by 7 centimeters.

    0
    2021-07-19T08:47:13+00:00

    Answer:

    Area = length  x width

    Area = (3width – 13) x width

    Area = 3 width^2 -13width

    56 = 3width^2 -13 width

    Width = 7

    Length = (3 *7) -13 = 8

    Step-by-step explanation:

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