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Answer :
The perimeter is found to be 46 inches.
To find the perimeter of the rectangle with an area of 120 square inches and sides represented by the expressions 2x-2 (length) and 3x (width), we first need to solve for x using the area formula for a rectangle, which is Area = Length * Width. We are given that the area is 120 square inches, so:
120 = (2x-2) *(3x).
Solving for x:
120 = 6x^2 - 6x
6x^2 - 6x - 120 = 0
x^2 - x - 20 = 0
Factoring the quadratic equation:
(x-5)(x+4) = 0
Thus, x = 5 (since x cannot be negative because it represents a length). Now substituting x back into the expressions for length and width:
Length = 2(5) - 2 = 8 inches
Width = 3(5) = 15 inches
Finally, we can find the perimeter using the formula Perimeter = 2 * (Length + Width):
Perimeter = 2* (8 + 15)
= 2 * 23
= 46 inches.
Therefore, the perimeter of the rectangle is 46 inches.
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