Question

solution
the length of a rectangle is twice its width. the perimeter of the rectangle is 36 ft.
what are the length and width of the rectangle? show your work.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) (in feet). Then the length \( l \) is twice the width, so \( l = 2w \).

Step2: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know the perimeter \( P = 36 \) ft. Substitute \( l = 2w \) into the formula:

$$ 36 = 2(2w + w) $$

Step3: Simplify and solve for \( w \)

First, simplify the expression inside the parentheses: \( 2w + w = 3w \). So the equation becomes:

$$ 36 = 2(3w) $$

$$ 36 = 6w $$

Divide both sides by 6:

$$ w = \frac{36}{6} = 6 $$

Step4: Find the length

Since \( l = 2w \), substitute \( w = 6 \):

$$ l = 2 \times 6 = 12 $$

Answer:

The width of the rectangle is 6 ft and the length is 12 ft.