A rectangle has a length that is twice its width. If the perimeter is 48 cm, wha

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Question: A rectangle has a length that is twice its width. If the perimeter is 48 cm, what is the width? (2022)

Options:

Correct Answer: 8 cm

Exam Year: 2022

Solution:

Let the width be w. Then the length is 2w. The perimeter is 2(w + 2w) = 48, which simplifies to 6w = 48, so w = 8 cm.

A rectangle has a length that is twice its width. If the perimeter is 48 cm, what is the width? (2022)

A rectangle has a length that is twice its width. If the perimeter is 48 cm, what is the width? (2022)

Step 1: Let the width of the rectangle be represented as 'w'.
Step 2: Since the length is twice the width, we can express the length as '2w'.
Step 3: The formula for the perimeter of a rectangle is P = 2(length + width).
Step 4: Substitute the expressions for length and width into the perimeter formula: P = 2(2w + w).
Step 5: Simplify the equation: P = 2(3w) = 6w.
Step 6: We know the perimeter is 48 cm, so set the equation equal to 48: 6w = 48.
Step 7: To find 'w', divide both sides of the equation by 6: w = 48 / 6.
Step 8: Calculate the value: w = 8 cm.

Perimeter of a Rectangle – Understanding how to calculate the perimeter using the formula P = 2(length + width) and applying it to a rectangle with given relationships between length and width.
Algebraic Manipulation – Using algebra to express relationships and solve for unknown variables, specifically setting up equations based on given conditions.