Question

the length of a rectangle is equal to one more than twice the width. what are the dimensions of the rectangle if the perimeter is 89 centimeters?

Explanation:

Step1: Define variables

Let the width be \( w \). Then the length \( l = 2w + 1 \).

Step2: Use perimeter formula

The perimeter formula for a rectangle is \( P=2(l + w) \). Substitute \( l = 2w + 1 \) and \( P = 89 \) into the formula:

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Step3: Solve for \( w \)

Subtract 2 from both sides: \( 89 - 2=6w \), so \( 87 = 6w \). Then \( w=\frac{87}{6}=14.5 \)

Step4: Solve for \( l \)

Substitute \( w = 14.5 \) into \( l = 2w + 1 \): \( l=2\times14.5+1=29 + 1=30 \)

Answer:

The width of the rectangle is \( 14.5 \) centimeters and the length is \( 30 \) centimeters.