Answer:
Just to make things easier, imagine that x is the length of the side of the square:
According to the information, we can conclude that:
2x + 5 (inches) is the length of the rectangle.
x - 6 (inches) is the width of the rectangle.
Since the areas of the square and the rectangle are the same, we know that:
(2x + 5)(x - 6) = x²
2x² - 12x + 5x - 30 = x²
2x² - 12x + 5x - x² = 30
x² - 7x - 30 = 0
x² + 3x - 10x - 30 = 0
x(x + 3) - 10(x + 3) = 0
(x - 10) (x +3) = 0
Now we can slove each part independently:
x - 10 = 0 or x + 3 = 0
x = 10 or x = -3
Since the length of the side of the square can't be a negative number, we can cancel -3 out and keep 10 only.
So the length of the side of the square is 10 inches.
(This is how I usually do to solve problems of this kind)
