Question

the length of a rectangle is twice its width. if the area of the rectangle is 50 cm², find its perimeter.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) cm. Then the length \( l = 2w \) cm (since length is twice the width).

Step2: Use area formula

The area of a rectangle is \( A = l \times w \). We know \( A = 50 \, \text{cm}^2 \), so substitute \( l = 2w \) into the area formula:
\( 50 = 2w \times w \)
\( 50 = 2w^2 \)

Step3: Solve for width

Divide both sides by 2: \( w^2 = \frac{50}{2} = 25 \)
Take the square root of both sides: \( w = \sqrt{25} = 5 \) (we take the positive root since width can't be negative)

Step4: Find length

Since \( l = 2w \), substitute \( w = 5 \): \( l = 2 \times 5 = 10 \) cm

Step5: Calculate perimeter

The perimeter \( P \) of a rectangle is \( P = 2(l + w) \). Substitute \( l = 10 \) and \( w = 5 \):
\( P = 2(10 + 5) = 2 \times 15 = 30 \)

Answer:

30