A square and rectangle have equal areas. The length of the rectangle is five inches more than twice the side of the square. The width of the rectangle is 6 inches less than the side of the square. Find the length of the side of the square.

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) = x²2x² - 12x + 5x - 30 = x²2x² - 12x + 5x - x²  = 30x² - 7x - 30             = 0 x² + 3x - 10x - 30    = 0x(x + 3) - 10(x + 3)   = 0(x - 10) (x +3)           = 0Now we can slove each part independently:x - 10 = 0 or x + 3 = 0x        = 10 or x      = -3Since 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)