A rectangle is cut into pieces and rearranged to form a square. Find perimeter of square.

Question

A rectangle with dimensions 9 inches and 16 inches is cut into pieces and rearranged to form a square. Find the perimeter of the square. Please help, thank you :)

Answer 1

The area must be maintained.

A_rectangle = 9(16), or 144

A_square = 144

side = 12 

perimeter = 48

Answer 2

It doesn't say anything about the dimensions of the pieces of the rectangle.  It seems reasonable to assume they are all equal pieces.

 

Then the smaller pieces are all 4.5" x 8" - half the dimensions of the original rectangle.  To form these pieces in a square tilt two opposite corner pieces 90 degrees and move all pieces slightly away until their edges line up.  This leaves a hole in the middle, but the outside of the new shape is a square.

 

The length of each side of this new square will be the sum of a longer side of a piece and a shorter side of a piece.  Thus the side of this new square is 12.5".

 

The formula for the perimeter of a square is 4 times s, where s is the length of a side.  The answer is then 4 x 12.5" = 50".