Arectangular balcony has a perimeter of 24 feet and an area of 27 square feet. what are the dimensions of the balcony?

Let x and y be the dimensions of the rectangular balcony.

The perimeter is 24 ft, therefore
2(x + y) = 24
or
x + y = 12                (1)

The area is 27 ft², therefore
xy = 27 
or
y = 27/x                  (2)

Substitute (2) into (1).
x + 27/x = 12
Multiply through by x.
x² + 27 = 12x
x² - 12x + 27 = 0
(x - 3)(x - 9) = 0
x = 3 or x = 9
When x = 3, y = 27/3 = 9
When x = 9, y = 27/9 = 3

The dimensions are 3ft by 9 ft.