Geometry/algebra 1

Use the given area A of the rectangle to find the value of x. Then give the dimensions of the rectangle.
A=91m^2
A=L•W
L=(2x+3)m
W=(x+2)m
91m^2=(2x+3)m•(x+2)m
91=(x+2)(2x+3)
Now what?

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  1. Set the equation equal to 0:

    2x^2 + 4x + 3x + 6 - 91 = 0

    2x^2 + 7x - 85 = 0

    Factor:

    (2x + 17) (x - 5) = 0

    Set the factors equal to 0:

    2x + 17 = 0; x = -17/2

    x - 5 = 0; x = 5

    You can't have a negative number for this problem, so use x = 5 for the value of x.

    I'll let you take it from here to determine the dimensions of the rectangle.

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