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
Answer:
The dimensions are 3ft by 9 ft.
