Question

the length of a rectangle is twice its width.
if the perimeter of the rectangle is 36 in, find its length and width.
length:
width:

Explanation:

Step1: Set up variables

Let the width of the rectangle be \( w \) inches. Then the length \( l = 2w \) inches.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P=2(l + w) \). Substitute \( l = 2w \) and \( P = 36 \) into the formula:

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Step3: Solve for \( w \)

Divide both sides of the equation \( 36 = 6w \) by \( 6 \):

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

Step4: Solve for \( l \)

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

$$l=2\times6 = 12$$

Answer:

length: \( 12 \) in
width: \( 6 \) in