Question

If the perimeter of a square is the same as that of an equilateral triangle of side length 24 cm, then what is the area of the square?

• A. 324 cm²
• B. 225 cm²
• C. 289 cm²
• D. 400 cm²

Answer 1

The Correct Option is A

Area of a Square Calculation 

- The perimeter of an equilateral triangle is given by:

\[ \text{Perimeter} = 3 \times \text{side length} \]

- Given that the side length of the triangle is 24 cm, the perimeter of the triangle is:

\[ 3 \times 24 = 72 \text{ cm} \]

- Since the perimeter of the square is the same as the perimeter of the triangle, the perimeter of the square is also 72 cm.

- The perimeter of a square is given by:

\[ \text{Perimeter} = 4 \times \text{side length of square} \]

Solving for the side length of the square:

\[ \text{Side length of square} = \frac{72}{4} = 18 \text{ cm} \]

- The area of the square is given by:

\[ \text{Area} = \text{(Side length)}^2 = 18^2 = 324 \text{ cm²} \]

Thus, the area of the square is 324 cm².

Conclusion: The correct answer is (a) 324 cm².