A rectangle has a length that is twice its width. If the perimeter of the rectan

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

Options:

Correct Answer: 12 cm

Solution:

Let the width be w. Then the length is 2w. The perimeter P = 2(length + width) = 2(2w + w) = 6w. Setting this equal to 48 gives 6w = 48, so w = 8 cm.

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

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

Step 1: Let the width of the rectangle be represented by the variable 'w'.
Step 2: Since the length is twice the width, we can express the length as '2w'.
Step 3: The formula for the perimeter (P) 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).
Algebraic Manipulation – Setting up equations based on relationships between length and width and solving for unknowns.