Question

the perimeter of a rectangle is 110 feet. find the length and width if the length is an integer and the width is 3 times the next consecutive integer.
answer
length = feet width = feet submit answer

Explanation:

Step1: Set up variables

Let the length be \(x\) (an integer). The next consecutive integer is \(x + 1\), and the width \(w=3(x + 1)\).

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \(P = 2(l+w)\). Given \(P = 110\), we substitute \(l=x\) and \(w = 3(x + 1)\) into the formula:

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Step3: Solve for \(x\)

Subtract 6 from both sides: \(110-6=8x\), so \(104 = 8x\). Then divide both sides by 8: \(x=\frac{104}{8}=13\).

Step4: Find the width

Since \(w = 3(x + 1)\), substitute \(x = 13\): \(w=3(13 + 1)=3\times14 = 42\).

Answer:

Length = \(13\) feet, Width = \(42\) feet