Question

the length of a rectangle is 2 in longer than its width. if the perimeter of the rectangle is 68 in, find its length and width.

Explanation:

Step1: Set up variables

Let the width of the rectangle be \(x\) inches. Then the length is \(x + 2\) inches.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \(P=2(l + w)\). Substituting \(P = 68\), \(l=x + 2\), and \(w=x\) into the formula:

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Step3: Solve for \(x\) (width)

Subtract 4 from both sides: \(68-4=4x\), so \(64 = 4x\). Then divide both sides by 4: \(x=\frac{64}{4}=16\)

Step4: Find the length

Since the length \(l=x + 2\), substitute \(x = 16\) into it. So \(l=16+2=18\)

Answer:

length: \(18\) in, width: \(16\) in