Question

the area of a rectangle is ( 2x^{2}-11x - 63 ) square units, and the length is ( 2x + 7 ) units. what is the perimeter, in units, of the rectangle?
( x - 9 )
( 2x - 18 )
( 3x - 2 )
( 6x - 4 )

Explanation:

Step1: Find the width of the rectangle

We know that the area of a rectangle \(A = l\times w\), where \(A = 2x^{2}-11x - 63\) and \(l=2x + 7\).
Factor \(2x^{2}-11x - 63\):

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Since \(A=l\times w=(2x + 7)\times w=(2x + 7)(x - 9)\), then \(w=x - 9\)

Step2: Calculate the perimeter of the rectangle

The perimeter of a rectangle \(P=2(l + w)\)
Substitute \(l = 2x+7\) and \(w=x - 9\) into the formula:

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Answer:

\(6x - 4\) (the fourth option)