The perimeter of the rectangle is 4x^2 +4x−16.
To find the perimeter of a rectangle with a given area and length, it is essential to first determine the width of the rectangle. The area (A) of a rectangle is the product of its length (L) and width (W), denoted as A=L×W. In this scenario, the provided area is 2x^2+6x−8, and the length is 2x−2.
By setting up the equation 2x^2 +6x−8=(2x−2)×W and solving for W, we obtain the expression for the width:
W= 2x^2 +6x−8/2x−2
Once the width is determined, the perimeter (P) of a rectangle is calculated using the formula P=2L+2W. Substituting the values for L and W into this formula, we get: P=4x^2 +4x−16
Thus, the perimeter of the rectangle is 4x^2+4x−16, incorporating both the given area and length.