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 area of the rectangle?

Options:

Correct Answer: 144 cm²

Solution:

Let width = w, then length = 2w. Perimeter = 2(l + w) = 48. Solving gives w = 8, l = 16. Area = l * w = 16 * 8 = 128 cm².

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

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

Step 1: Let the width of the rectangle be represented as 'w'.
Step 2: Since the length is twice the width, we can write 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: Solve for 'w' by dividing both sides by 6: w = 48 / 6 = 8 cm.
Step 8: Now, find the length by substituting 'w' back into the length equation: length = 2w = 2 * 8 = 16 cm.
Step 9: To find the area of the rectangle, use the formula: Area = length * width.
Step 10: Substitute the values for length and width: Area = 16 * 8.
Step 11: Calculate the area: Area = 128 cm².

Perimeter of a Rectangle – Understanding how to calculate the perimeter using the formula P = 2(l + w) and applying it to find dimensions.
Area of a Rectangle – Calculating the area using the formula A = l * w after determining the length and width.
Algebraic Manipulation – Setting up equations based on relationships between length and width and solving for unknowns.