Question 749122
Perimeter = 2 * length + 2 * width
Area      = length * width
If we make length = x and width = y
then Perimeter = 2x + 2y
     Area      = xy
Make two equations:

        2x + 2y = 22...1
             xy = 24...2

Rearrange xy = 24 => x = 24/y
Substitute x = 24/y  into (1)

       2(24/y) + 2y = 22
         48/y  + 2y = 22

 Take to one denominator - y

         48 + 2y^2 = 22y
Sort out 2y^2 - 22y + 48 = 0
         divide by 2
          y^2 - 11y + 24 = 0
          (y - 3)(y - 8) =0

So y = 3 or y = 8
Substituting in 2x + 2y = 22
                2x + 2(3) = 22
                     2x = 22 - 6
                     2x = 16
                      x = 8
                 2x + 2y = 22
                 2x + 16 = 22
                      2x = 22 - 16
                      2x = 6
                       x = 3

            So either length is 8m and width is 3m
                   or length is 3m and width is 8m