The length of Joe's rectangular garden is 1 meter less than twice its width, and its area is 120m^2. Find the dimensions of the garden by setting up a quadratic equation and define its variables.
A = l*w
l = 2w -1
120 = (2w-1)w
120 = 2w^2 -w
2w^2 -w -120 = 0
To solve this problem, let's define the variables first:
Let's say the width of Joe's garden is w meters. Since the length is 1 meter less than twice its width, the length can be represented as 2w - 1 meters.
Now, we can set up the equation based on the given information:
Area of the garden = Length × Width
Since the area of the garden is given as 120m^2, we can write:
120 = (2w - 1) × w
Simplifying the equation, we have:
120 = 2w^2 - w
Now, let's rearrange the equation to form a quadratic equation in standard form:
2w^2 - w - 120 = 0
This is a quadratic equation since it can be written in the form: ax² + bx + c = 0, where a = 2, b = -1, and c = -120.