Question

the length of a rectangle is twice its width. if the perimeter of the rectangle is 30 in, find its length and width. length: in width: in

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 \( P = 30 \) into the formula:

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Step3: Solve for \( w \)

Divide both sides of the equation \( 30 = 6w \) by 6:

$$ w=\frac{30}{6}=5 $$

Step4: Solve for \( l \)

Since \( l = 2w \), substitute \( w = 5 \) into the equation: \( l=2\times5 = 10 \)

Answer:

length: \( 10 \) in, width: \( 5 \) in