A rectangle has a length that is twice its width. If the perimeter of the rectangle is 36 units, what is the width of the rectangle? - Treasure Valley Movers

How to Solve Rectangle Problems: Finding the Width When Length is Double the Width

Understanding basic geometry principles helps solve many problems involving rectangles—especially when dimensions follow simple ratios. One common question is: If a rectangle has a length that is twice its width and a perimeter of 36 units, what is the width? This article breaks down the math behind the problem with clear steps, making it easy for students and math enthusiasts alike.

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Understanding the Rectangle’s Dimensions

A rectangle has two consistent measurements: length and width. According to the problem, the length is twice the width. We can express this relationship using algebra:

Let the width = w
Then the length = 2w

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Using the Perimeter Formula

The perimeter P of a rectangle is calculated with the formula:
P = 2 × (length + width)

Substituting the values we have:
36 = 2 × (2w + w)

Simplify inside the parentheses:
36 = 2 × (3w)
36 = 6w

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Solving for the Width

To find w, divide both sides of the equation by 6:
w = 36 ÷ 6
w = 6

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Verifying the Answer

We now know the width is 6 units. Since length = 2 × width, the length is:
2 × 6 = 12 units

Calculate the perimeter to confirm:
P = 2 × (12 + 6) = 2 × 18 = 36 units, which matches the given value.

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Final Answer

The width of the rectangle is 6 units.

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