The diagonal of a square is 12\sqrt{2} cm and the area of an equilateral triangle is 64\sqrt{3} square cm. Which of the following statements is/are correct?<br>1. The square and the triangle have the same perimeter.<br>2. Four times the area of the square is equal to 3\sqrt{3} times the area of the triangle.<br>Select the correct answer using the code given below.
- A. 1 only
- B. 2 only
- C. Both 1 and 2 ✓
- D. Neither 1 nor 2
Correct Answer: C. Both 1 and 2
Explanation
Square side = 12, perimeter = 48, area = 144. Triangle area \frac{\sqrt{3}}{4}a^2 = 64\sqrt{3} \implies a=16, perimeter = 48. Statement 1 is true. Four times square area = 4 \times 144 = 576. 3\sqrt{3} \times (64\sqrt{3}) = 3 \times 3 \times 64 = 576. Statement 2 is true.
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