Question

the perimeter of a rectangle is 40 inches. find the length and width if the length is an integer and the width is 2 times the next consecutive integer. answer length = inches width = inches submit answer

Explanation:

Step1: Set up variables

Let the length be \(x\) (an integer). The next consecutive integer is \(x + 1\), and the width \(w=2(x + 1)\).

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \(P = 2(l+w)\). Given \(P = 40\), we substitute \(l=x\) and \(w = 2(x + 1)\) into the formula:

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Step3: Solve for \(x\)

Subtract \(4\) from both sides: \(40-4=6x\), so \(36 = 6x\). Then divide both sides by \(6\): \(x=\frac{36}{6}=6\).

Step4: Find the width

If \(x = 6\), then \(w=2(x + 1)=2\times(6 + 1)=14\).

Answer:

Length \(=6\) inches, Width \(=14\) inches