A rectangular 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

Answer:

The dimensions are 3ft by 9 ft.