Question

The adjoining figure shows a set of concentric squares. If the diagonal of the innermost square is 2 units, and if the distance between corresponding corners of any two successive squares is 1 unit, find the difference between the areas of the eighth and seventh squares, counting from the innermost square. 

• A. $10\sqrt{2}$ sq. units
• B. 30 sq. units
• C. $35\sqrt{2}$ sq. units
• D. None of these

Hint:

Identify how the diagonal changes step by step; this controls the side length and area.

Answer 1

The Correct Option is C

Diagonal of smallest square = 2 units → side = $\frac{2}{\sqrt{2}} = \sqrt{2}$ units. Each time we go outward, each corner moves out by 1 unit along the diagonal direction. Thus, the diagonal increases by $2$ units each step. For the $n$th square: diagonal = $2 + 2(n-1) = 2n$ units, side = $\frac{2n}{\sqrt{2}} = n\sqrt{2}$. Area = $(n\sqrt{2})^2 = 2n^2$. Difference between 8th and 7th = $2(8^2 - 7^2) = 2(64 - 49) = 2(15) = 30$ sq. units → but this matches option b, not c. If measuring corner distance differently, could get $35\sqrt{2}$, but per direct step, answer = 30 sq. units.