2024 · Q82
There are n concentric squares. The area of the innermost square is 1 unit and the distance between corresponding corners of any two consecutive squares is 1 unit. Consider the following statements :
- IThe diagonal of the nth square is 2n + √2 − 2
- IIThe area included between nth square and (n - 1)th square is independent of n Which of the statements given above is/are correct?
Elementary MathematicsQuadrilaterals and Polygons
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
Side s_n = 1+(n−1)√2 (each step adds √2 along the half-diagonal), so diagonal = √2·s_n = 2n+√2−2: statement I is correct. The ring area s_n²−s_{n−1}² = 2√2+2(2n−3) depends on n: statement II is false. Only I — option A.