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

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Accepted Answer

30 sq. units — The diagonal of the innermost square is 2 units. The diagonal of every successive square would increase by 2 units (since corners are one unit apart). So the diagonal of the 7th square = 14 units and that of the 8th square = 16 units. Areas of the 7th square = 1 2 (14) 2 and that of 8th square = 1 2 (16) 2 , and 128 respectively. Hence, the difference in their areas = (128 &ndash; 98) = 30 sq.units.

CAT 1997 — QA Question 32

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