The length of a rectangle is five more than its width. if the perimeter is 120, find both the length and the width.

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Answer to a math question The length of a rectangle is five more than its width. if the perimeter is 120, find both the length and the width.

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Neal

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105 Answers

Let's represent the width of the rectangle as $w$.

According to the problem, the length is five more than the width, so we can write the equation: length = $w+5$.

The perimeter of a rectangle is equal to twice the sum of its length and width. So, the equation for the perimeter is: $2(w + (w+5)) = 120$.

Simplifying the equation:
$2(2w + 5) = 120 \implies 4w + 10 = 120$.

Subtracting 10 from both sides:
$4w = 110$.

Dividing by 4 on both sides:
$w = 27.5$.

Thus, the width of the rectangle is 27.5.

To find the length, we substitute the value of $w$ back into the equation:
length = $w + 5 = 27.5 + 5 = 32.5$.

Answer: The width of the rectangle is 27.5 units, and the length is 32.5 units.

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