Math CentralQuandaries & Queries


Question from Rajesh, a student:

There are 10 squares drawn one inside another.The diagonal of the inneremost square is 20 units. if the distance b/w the corresponding corners of any two successive squares is 1 unit, find the diffrence between the areas of the eigth and seventh square counting from the innermost

Hi Rajesh.

The length of the diagonal of a square is SQRT(2) times the length of a side. You can prove this to yourself by using the Pythagorean Theorem. Therefore the area of the square is A = D2/2, where D is the length of the diagonal.

So add up the length of the diagonals of each of the two squares, calculate the areas and subtract.

Stephen La Rocque

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