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.
Explanation:
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 = 12 (14)2 and that of 8th square = 12(16)2, and 128 respectively. Hence, the difference in their areas = (128 – 98) = 30 sq.units.
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