Awire in the shape of a rectangle whose width is 22 cm, is bent to form a square of side 31 cm. find the length of the rectangle.

The wire must have the same total length. In other word, the perimeter of the rectangle wire is the same as the perimeter of square wire.

perimeter of rectangle = perimeter of square
2(l + w) = 4s
2(l + 22) = 4(31)
2l + 44 = 124
2l = 124 - 44
2l = 80
  l = 80/2
  l = 40
The length of the rectangle is 40 cm

We can find this by finding the perimeter of the square.
31×4= 124
Now the rectangle has two sets of parallel lines. There are two lines that are 22 cm, which comes out to 44 cm. We can subtract 44 from the perimeter to find the total of the length doubled.
124-44
80÷2
40
So, the length of the rectangle is 40 cm.