A square sheet is formed by joining n identical square sheets of same size. If the length of the diagonal of the bigger square sheet so formed is m, then what is the side length of a smaller square sheet?
- A. \frac{m}{\sqrt{n}}
- B. \frac{m}{2\sqrt{n}}
- C. \frac{m}{\sqrt{2n}} ✓
- D. \frac{\sqrt{2}m}{\sqrt{n}}
Correct Answer: C. \frac{m}{\sqrt{2n}}
Explanation
Let the side of the small square be a. Area of small square = a^2. Total area = n \times a^2. The big square has side S = a\sqrt{n}. The diagonal of the big square is m = S\sqrt{2} = a\sqrt{2n}. Therefore, a = \frac{m}{\sqrt{2n}}.
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