A gardener wants to create a rectangular vegetable garden in a backyard. She wants it to have a total area of 180 square feet, and it should be 3 feet longer than it is wide. What dimensions should she use for the vegetable garden? (Area = length * width)(1 point)
Let's assume the width of the vegetable garden is x feet.
According to the information given, the length of the vegetable garden would be (x + 3) feet.
The area of the vegetable garden is the product of its length and width, so:
Area = (x + 3) * x = 180
Expanding the equation, we have:
x^2 + 3x = 180
Rearranging the equation to standard form, we have:
x^2 + 3x - 180 = 0
Now we can factorize the quadratic equation:
(x - 12)(x + 15) = 0
Setting each factor equal to zero, we get:
x - 12 = 0 or x + 15 = 0
x = 12 or x = -15 (ignoring the negative value as it is not possible in this context)
Therefore, the width of the vegetable garden is 12 feet.
The length would be 12 + 3 = 15 feet.
So, the dimensions of the vegetable garden should be 12 feet by 15 feet.