Question

Column A: The perimeter of a square with sides of length 5 
Column B: The perimeter of a rectangle with length 10 and width 2

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

Always double-check that you are using the correct formula. It's a common mistake to calculate the area (length × width) instead of the perimeter.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question requires the calculation and comparison of the perimeters of two different geometric shapes: a square and a rectangle.
Step 2: Key Formula or Approach:
The formulas for the perimeters are:
- Perimeter of a square = \( 4 \times \text{side length} \)
- Perimeter of a rectangle = \( 2 \times (\text{length} + \text{width}) \)
Step 3: Detailed Explanation:
Column A: We calculate the perimeter of the square.
Side length = 5.
\[ \text{Perimeter} = 4 \times 5 = 20 \] So, the quantity in Column A is 20.
Column B: We calculate the perimeter of the rectangle.
Length = 10 and Width = 2.
\[ \text{Perimeter} = 2 \times (10 + 2) = 2 \times 12 = 24 \] So, the quantity in Column B is 24.
Comparison:
We compare 20 (Column A) with 24 (Column B).
Since \(20<24\), the quantity in Column B is greater.
Step 4: Final Answer:
The perimeter of the square is 20 and the perimeter of the rectangle is 24. Therefore, the quantity in Column B is greater.