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) Responses 12 feet by 15 feet 12 feet by 15 feet 3 feet by 60 feet 3 feet by 60 feet 3 feet by 180 feet 3 feet by 180 feet 15 feet by 18 feet
Let's call the width of the garden x. According to the given information, the length of the garden is 3 feet longer than the width, so it is x + 3.
The area of the garden is the product of its length and width, which is (x + 3) * x = x^2 + 3x.
We know that the area of the garden is 180 square feet, so we can set up the equation x^2 + 3x = 180.
Rearranging the equation, we get x^2 + 3x - 180 = 0.
Now we can solve this quadratic equation by factoring or using the quadratic formula. The factored form of the equation is (x - 12)(x + 15) = 0.
Setting each factor equal to zero, we have x - 12 = 0 or x + 15 = 0.
Solving these equations separately, we find x = 12 or x = -15. Since the width of the garden cannot be negative, we discard x = -15.
Therefore, the width of the garden is x = 12 feet, and the length is x + 3 = 12 + 3 = 15 feet.
So the dimensions for the vegetable garden should be 12 feet by 15 feet.