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18 February, 21:52

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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  1. 18 February, 22:15
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    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.
  2. 18 February, 22:20
    0
    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
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