SOLUTION: 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 six squares, find the sum of
Algebra ->
Sequences-and-series
-> SOLUTION: 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 six squares, find the sum of
Log On
Question 982081: 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 six squares, find the sum of the areas of all squares
in square inches.thank you Answer by Edwin McCravy(20055) (Show Source):
Look at this:
8 congruent isosceles right triangles make up the big outer
square, and only 4 of them make up the inner (diamond-shape)
square, joining the midpoints of the consecutive
sides of the outer square.
That means each square will have 1/2 as much area as the preceding square.
The area of the first square is 82=64 and the next square will
have half that area or 32.
Now you can do the problem. It will be 64 + 32 + ? + ? + ? + ? = ?
Edwin
