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
