SOLUTION: a square piece of paper is cut into six rectangle pieces when the perimeter lengths of the six pieces are added together the result is 120cm what is the area of the square piece

There are many different solutions to this problem,
depending on how you cut the rectangle

If you cut it into equal rectangles like this:



where each has perimeter 2L+2W,

then the sum of the perimeters is 6(2L+2W)
6(2L+2W) = 120
 12L+12W = 120
     L+W = 10
       L = 10-W

      3W = 2L
      3W = 2(10-W)
      3W = 20-2W
      5W = 20
       W = 4 
       L = 10-W
       L = 10-4
       L = 6

So the a side of the square is 3W = 2L = 3(4) = 2(6) = 12

So the area of a 12×12 square is 144cm²

-----------------------------------------------------

However if you cut it into 6 equal pieces lke this,
which is what the other tutor did, you get a smaller area.



Then up to a certain point, it's like the above:

where each has perimeter 2L+2W,

then the sum of the perimeters is 6(2L+2W)
6(2L+2W) = 120
 12L+12W = 120
     L+W = 10
       L = 10-W

But this time

      6W = L  

      6W = 10-W
      7W = 10
       W = 10/7

And the side of the square is L = 6W = 6(10/7) = 60/7 cm

And the area of the square is (60/7)² = 3600/49 = 73.46938776 cm². 
 
-------------------------------------------------------------

Now if you cut into 6 UNequal rectangles like this




You would get still a totally different answer.

Edwin