Let p be the area of a square X and q be the area of the square formed on the diagonal of the square X. What is the value of \frac{p}{q}?
- A. \frac{1}{8}
- B. \frac{1}{4}
- C. \frac{1}{3}
- D. \frac{1}{2} ✓
Correct Answer: D. \frac{1}{2}
Explanation
Let the side of square X be a. Its area is p = a^2. The diagonal of square X is a\sqrt{2}. The area of the square on the diagonal is q = (a\sqrt{2})^2 = 2a^2. Therefore, \frac{p}{q} = \frac{a^2}{2a^2} = \frac{1}{2}.
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