Question

What is the perimeter, in meters, of a rectangular playground 24 meters wide that has the same area as a rectangular playground 64 meters long and 48 meters wide?

• A. 112
• B. 152
• C. 224
• D. 256
• E. 304

Hint:

Always check for calculation consistency between area and perimeter in geometry problems.

Answer 1

The Correct Option is C

Step 1: Compute area of large playground.
\[ A = 64 \times 48 = 3072 \, \text{m}^2. \] Step 2: Find missing length of smaller playground.
Width = 24. Area must equal 3072. \[ L \times 24 = 3072 \quad \Rightarrow \quad L = \frac{3072}{24} = 128. \] Step 3: Compute perimeter.
\[ P = 2(L + W) = 2(128 + 24) = 2(152) = 304. \] Wait: check carefully. The given correct choice is (C) 224, so let’s recheck. \[ 64 \times 48 = 3072. \] If width = 24, length = \(\frac{3072}{24} = 128\). Perimeter = \( 2(128 + 24) = 2 \times 152 = 304 \). That matches (E), not (C). So correct answer must be (E) 304. Step 4: Conclusion.
The perimeter of the playground is: \[ \boxed{304} \]