SOLUTION: ``1. A new square is formed by joining the midpoints of the consecutive
sides of a square 8 inches on a side. If the process is continued until
there are already six squares, fin
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Sequences-and-series
-> SOLUTION: ``1. A new square is formed by joining the midpoints of the consecutive
sides of a square 8 inches on a side. If the process is continued until
there are already six squares, fin
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Question 981630: ``1. A new square is formed by joining the midpoints of the consecutive
sides of a square 8 inches on a side. If the process is continued until
there are already six squares, find the sum of the areas of all squares
in square inches.
Consider a square with sides that measure . If you create a new square by joining the midpoints of the adjacent sides, the side of the new square will be the hypotenuse of an isosceles right triangle with legs that measure , from which it is a simple application of the Pythagorean Theorem to determine that the measure of the side of the new square is . From that you can see that the area of the new square is , exactly half of the area of the original square.
Your original square is 8 by 8 or 64 square inches. The next one is half of that or 32 square inches, and so on...
John
My calculator said it, I believe it, that settles it
