Arectangular balcony has an area of 21 square feet and a perimeter of 20 feet. what are the dimensions of the balcony?

Write an equation system by the problem
We can write "Area of rectangular balcony is 21 square feet" as
∴ area = 21
∴ l × w = 21   (first equation)

We can write "The perimeter is 20 feet" as
∴ perimeter = 20
∴ 2(l + w) = 20   (second equation)

Simplify the second equation to find w in the value of l
2(l + w) = 20
l + w = 20/2
l + w = 10
w = 10 - l

Use subtitution method to solve the problem. Input w as (10 - l) to the first equation
l × w = 21
l × (10 - l) = 21
10l - l² = 21
(multiply the two sides by -1)
l² - 10l = -21
l² - 10l + 21 = 0
(l - 7)(l - 3) = 0
l = 7 or l = 3

The length of the rectangle is either 7 or 3

Find the width
If the length of the rectangle is 7, then the width will be
w = 10 - l
w = 10 - 7
w = 3
The dimension will be 7 × 3 

If the length of the rectangle is 3, then the width will be
w = 10 - l
w = 10 - 3
w = 7
The dimension will be 3 × 7