The length of one of the sides of a square was increased by 4 dm, and the other one was decreased by 6 dm. As a result, a rectangle was made

Question

The length of one of the sides of a square was increased by 4 dm, and the other one was decreased by 6 dm. As a result, a rectangle was made with an area of 56 dm2. Find the length of the side of the square

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Remi 2 weeks 2021-11-15T12:59:56+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-15T13:01:08+00:00

    Answer:the length of the side of the square is 10 dm

    Step-by-step explanation:

    Let x represent the length of each side of the square.

    The length of one of the sides of a square was increased by 4 dm, and the other one was decreased by 6 dm. This means that the length of one side of the rectangle formed is (x + 4) dm and the length of the other side of the rectangle is

    (x – 6) dm

    The are of the rectangle is 56dm². This means that

    (x – 6)(x + 4) = 56

    x² + 4x – 6x – 24 = 56

    x² – 2x – 24 – 56 = 0

    x² – 2x – 80 = 0

    x² + 8x – 10x – 80 = 0

    x(x + 8) – 10(x + 8) = 0

    x – 10 = 0 or x + 8 = 0

    x = 10 or x = – 8

    Since the length of each side of the square cannot be negative, then

    x = 10

    0
    2021-11-15T13:01:21+00:00

    Answer:

    The answer to your question is 10 dm

    Step-by-step explanation:

    Data

    length of a rectangle = x + 4

    height of a rectangle = x – 6

    Area of the rectangle = 56 dm²

    length of the square = x

    Process

    1.- Find x with the information given for the rectangle

        Area = length x height

    Substitution

        56 = (x + 4)(x – 6)

    Expand

        56 = x² – 2x – 24

    Equal to zero

                x² – 2x – 24 – 56 = 0

    Simplify

                 x² – 2x – 80 = 0

    Factor

                (x – 10)(x + 8) = 0

    Equal to zero

                 x₁ -10 = 0          x₂ + 8 = 0

                 x₁ = 10               x₂ = -8

    2.- Conclusion

    The length of the square is 10 dm because there are no negative lengths.                  

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