Question

question
the length and width of a rectangle are consecutive odd integers. the perimeter of the rectangle is 96 centimeters. find the length and width of the rectangle
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Explanation:

Step1: Let the width be \(x\)

Since the length and width are consecutive odd integers, let the width \(x\) (odd), then the length is \(x + 2\) (the next odd integer).

Step2: Use the perimeter formula

The perimeter formula of a rectangle is \(P=2(l + w)\). Given \(P = 96\), substitute \(l=x + 2\) and \(w=x\) into the formula: \(96=2((x + 2)+x)\).
Simplify the equation:

$$
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Step3: Find the length and width

If \(x = 23\) (width), then the length \(x + 2=23+2 = 25\).

Answer:

The width of the rectangle is \(23\) centimeters and the length is \(25\) centimeters.