Questions: The length of a rectangle is twice its width. If the perimeter of the rectangle is 36 cm, find its area.

The length of a rectangle is twice its width. If the perimeter of the rectangle is 36 cm, find its area.
Transcript text: The length of a rectangle is twice its width. If the perimeter of the rectangle is 36 cm, find its area.
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Solution

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Solution Steps

Step 1: Define the variables

Let the width of the rectangle be \( w \) cm. Since the length is twice the width, the length \( l \) is \( 2w \) cm.

Step 2: Write the perimeter formula

The perimeter \( P \) of a rectangle is given by: \[ P = 2(l + w) \] Substitute the given perimeter \( P = 36 \) cm and the expression for \( l \): \[ 36 = 2(2w + w) \]

Step 3: Solve for the width \( w \)

Simplify the equation: \[ 36 = 2(3w) \] \[ 36 = 6w \] Divide both sides by 6: \[ w = 6 \text{ cm} \]

Step 4: Find the length \( l \)

Since \( l = 2w \), substitute \( w = 6 \) cm: \[ l = 2 \times 6 = 12 \text{ cm} \]

Step 5: Calculate the area

The area \( A \) of the rectangle is given by: \[ A = l \times w \] Substitute \( l = 12 \) cm and \( w = 6 \) cm: \[ A = 12 \times 6 = 72 \text{ cm}^2 \]

The area of the rectangle is \( 72 \) cm².

Final Answer

\(\boxed{72 \text{ cm}^2}\)

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