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, find
Algebra.Com
Question 981574: 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.
2.In President Sergio Osmeña High School, suspension of classes is
announced through text brigade. One stormy day, the principal
announces the suspension of classes to two teachers, each of whom
sends this message to two other teachers, and so on. Suppose that
text messages were sent in five rounds, counting the principal’s text
message as the first, how many text messages were sent in all?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
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
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