Each side of a square is 4 square meters long. When each side is increased by X meters, the area is doubled. Find the value of X.

Question

Setup using a quadratic equation, then solve the problem

Answer 1

The length of a side of the second rectangle is (4 + x).  The area if the second square is 32.

 

Thus, (4 + x)² = 32

          16 + 8x + x² = 32

 

If we solve by completing the square:

 

          x² + 8x = 16

          x² + 8x + 16 = 16 + 16

          (x + 4)² = 32

           abs. value (x + 4) = sqrt 32

                x + 4 = 4sqrt2 or -4sqrt2

                x = (4sqrt2 - 4) or (-4sqrt2 - 4)

 

Since x represents the length of a side of a square it can not be the negative number (-4sqrt2 - 4)

 

Thus x = 4sqrt2 - 4.