The length of Joe's rectangular garden is 1 meter less than its width and its area is 120m^2. Find the dimensions of the garden.
Setup a quadratic equation to find the dimensions of the garden.
A = LW
L = w-1
120 =(w-1)w
120 = w^2-w
w^2-w-120 =0
How do I solve for w with that quadratic equation? I can't factor it right?
19
To find the dimensions of Joe's rectangular garden, let's use algebra.
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.