Question

a rectangle has a length that is 2 more than twice the width. its perimeter is 36 inches. which equation models this? 2x - 2 = 36 x - 2x - 2 = 36 2(x) - 2x - 2 = 36 2(x) - 2(2x - 2) = 36

Explanation:

Step1: Let width be \(x\)

Let the width of the rectangle be \(x\) inches.

Step2: Express length in terms of \(x\)

The length is 2 more than twice the width, so length \(l = 2x + 2\).

Step3: Use perimeter formula

The perimeter formula for a rectangle is \(P=2(l + w)\). Given \(P = 96\), substituting \(l = 2x+2\) and \(w=x\) into the formula, we get \(96=2((2x + 2)+x)\). Simplifying the right - hand side: \(2((2x + 2)+x)=2(2x+2+x)=2(3x + 2)=6x+4\). Another way is to expand \(2(l + w)\) as \(2l+2w\), so \(2(2x + 2)+2x=4x + 4+2x=6x + 4\). If we expand it in the form of \(2(x+(2x + 2))=2x+2(2x + 2)=2x+4x + 4=6x+4\). But if we consider the formula \(P = 2l+2w\) directly and substitute \(l = 2x+2\) and \(w = x\), we have \(2x+2(2x + 2)=96\), which is \(2x+4x + 4=96\) or \(2(x)+2(2x + 2)=96\).

Answer:

The correct equation is \(2(x)+2(2x + 2)=96\) (the last option in the original multiple - choice list, although the list items are not clearly labeled).