Answer:the length is 12.6 yards and the width is 9.6 yards
Step-by-step explanation:
Let L represent the length of the garden.
Let W represent the width of the garden.
The formula for determining the area of a rectangle is expressed as
Area = Length × width
A rectangular garden covers 120 yd^2. It means that
LW = 120 - - - - - - - - - - - - 1
The length is 3yd longer than the width. This means that
L = W + 3
Substituting L = W + 3 into equation 1, it becomes
W(W + 3) = 120
W² + 3W = 120
W² + 3W - 120 = 0
Applying the general formula for solving quadratic equations,
x = [- b ± √(b² - 4ac)]/2a
W = [- 3 ± √(3² - 4 × 1 × - 120)]/2 × 1
W = [- 3 ± √(9 + 480)]/2
W = (- 3 ± √489)/2
W = (- 3 ± 22.11)/2
W = 19.11/2 or W = - 25.11/2
W = 9.6 or W = - 12.6
L = W + 3 = 9.6 + 3
L = 12.6
