A = LW
L = w-1
120 =(w-1)w
120 = w^2-w
w^2-w-120 =0
Setup a quadratic equation to find the dimensions of the garden.
L = w-1
120 =(w-1)w
120 = w^2-w
w^2-w-120 =0
Let's assume that the width of the garden is "x" meters. According to the given information, the length of the garden is 1 meter less than its width, so the length can be represented as "x - 1" meters.
The area of the garden is given as 120m^2. The formula for calculating the area of a rectangle is length multiplied by width, so we can set up the following equation:
Area = Length * Width
120 = (x - 1) * x
To solve this equation, we need to distribute and combine like terms:
120 = x^2 - x
Now, let's move all the terms to one side of the equation to set it equal to zero:
x^2 - x - 120 = 0
This is a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = -1, and c = -120.
We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case.
Factor the quadratic equation into two binomial factors:
(x - 12)(x + 10) = 0
Now, we can set each factor equal to zero and solve for x:
x - 12 = 0 or x + 10 = 0
Solving for x in each case gives us:
x = 12 or x = -10
Since the width of the garden cannot be negative, we can disregard the solution x = -10.
Therefore, the width of Joe's rectangular garden is 12 meters. To find the length, we can substitute this value back into the equation for the length:
Length = x - 1 = 12 - 1 = 11 meters
So, the dimensions of the garden are 12 meters by 11 meters.