Question 1084371
the area of the rectangle is 54 square meters.


if the length is 2 meters less and the width is 1 meter more, it will have been a square.


assume the length of the rectangle is x and the width of the rectangle is y.


in order for it to be a square, you need to shorten the length by 2 meters and increase the width by 1 meter.


you would get x-2 is the length and y + 1 is the width.


if it is now a square, then x-2 = y+1 because all sides are equal in a square.


you can solve for y to get y = x-3


go back to your rectangle.


the area is 54 square meters which is equal to x * y.


since y is equal to x-3, you get x * (x-3) = 54


simplify to get x^2 - 3x = 54


subtract 54 from both sides to get x^2 - 3x - 54 = 0


factor to get (x-9) * (x+6) = 0


solve for x to get x = 9 or x = -6


x can't be negative so x has to be 9


since x * y = 54, when x = 9, y has to be equal to 6


you get x * y = 9 * 6 = 54


it's a rectangle.


if you subtract 2 from the length and add 1 to the width, you get:


(9-2) * (6+1) = 7 * 7 = 49


it's now a square with each side equal to 7 and the area of the square is 49 square meters.