Question

A rectangular field is 400 feet long and 300 feet wide. If a square field has the same perimeter as the rectangular field, what is the length, in feet, of each side of the square field?

• A. 175
• B. 350
• C. 200\(\sqrt{2}\)
• D. 350\(\sqrt{2}\)
• E. 100\(\sqrt{3}\)

Hint:

Be careful not to confuse perimeter with area. A common mistake is to calculate the area of the rectangle and then try to find the side of a square with the same area. Read the question carefully to identify the correct property (perimeter, in this case).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a straightforward geometry problem involving the calculation of perimeters for a rectangle and a square.
Step 2: Key Formula or Approach:
1. Use the formula for the perimeter of a rectangle: \(P = 2(l + w)\).
2. Use the formula for the perimeter of a square: \(P = 4s\).
3. Set the two perimeters equal to each other and solve for the side of the square, \(s\).
Step 3: Detailed Explanation:
First, calculate the perimeter of the rectangular field. - Length (\(l\)) = 400 ft - Width (\(w\)) = 300 ft - Perimeter of rectangle = \(2 \times (400 + 300) = 2 \times 700 = 1400\) ft. Next, use this perimeter to find the side length of the square field. - Perimeter of square = 1400 ft. - We know that \(P_{square} = 4s\), where \(s\) is the side length. - So, \(4s = 1400\). - Divide by 4: \(s = \frac{1400}{4} = 350\) ft. Step 4: Final Answer:
The length of each side of the square field is 350 feet.