If the area of the rectangle is 264 m², calculate the perimeter.
Understand the Problem
The question asks us to calculate the perimeter of a rectangle given its area of 264 m² and one side length of 24 m. To find the perimeter, we first need to determine the missing side length using the area formula for rectangles, which is Area = length × width.
Answer
The perimeter is \( 70 \, \text{m} \).
Answer for screen readers
The perimeter of the rectangle is ( 70 , \text{m} ).
Steps to Solve
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Identify the Area Formula The area of a rectangle is given by the formula: $$ \text{Area} = \text{length} \times \text{width} $$ Here, the area is 264 m² and one side (length) is 24 m.
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Calculate the Missing Side Length (Width) To find the width, rearrange the area formula to solve for width: $$ \text{width} = \frac{\text{Area}}{\text{length}} = \frac{264 \text{ m}^2}{24 \text{ m}} $$ Calculating gives: $$ \text{width} = 11 \text{ m} $$
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Calculate the Perimeter The perimeter of a rectangle is calculated using the formula: $$ \text{Perimeter} = 2 \times (\text{length} + \text{width}) $$ Substituting the values: $$ \text{Perimeter} = 2 \times (24 \text{ m} + 11 \text{ m}) $$
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Perform the Addition and Final Calculation First, add the length and width: $$ 24 \text{ m} + 11 \text{ m} = 35 \text{ m} $$ Now calculate the perimeter: $$ \text{Perimeter} = 2 \times 35 \text{ m} = 70 \text{ m} $$
The perimeter of the rectangle is ( 70 , \text{m} ).
More Information
The perimeter is the total distance around the rectangle. In this case, we used the area to find the missing width, which allowed us to compute the perimeter accurately.
Tips
- Forgetting to convert the area to width before calculating.
- Misapplying the perimeter formula by not doubling the sum of length and width.
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