Question

The mayor of Grayson is planting a garden in the city park. Originally, the plan was to build a square garden, however, the length of the garden was increased by 6 feet. The total area of the garden is 112 square feet. Use factoring, completing the square, or the quadratic formula to solve for the dimensions of the garden.

a) Factoring, Dimensions: Length 10 feet, Width 16 feet
b) Completing the square, Dimensions: Length 16 feet, Width 10 feet
c) Quadratic formula, Dimensions: Length 10 feet, Width 16 feet
d) Factoring, Dimensions: Length 16 feet, Width 10 feet

Answer 1

The dimensions of the garden are: Length 10 feet, Width 16 feet.

Step-by-step explanation:

In this problem, the original plan was to build a square garden. However, the length of the garden was increased by 6 feet. Let's assume the original length of the garden is x feet. Since the length was increased by 6 feet, the new length is x + 6 feet. The total area of the garden is given as 112 square feet.

To solve for the dimensions of the garden, we can set up the equation x(x + 6) = 112. This equation represents the area of the garden. To solve it, we can use factoring, completing the square, or the quadratic formula. Let's use factoring:

1. First, rewrite the equation as x^2 + 6x - 112 = 0.
2. Factor the equation as (x + 16)(x - 10) = 0.
3. Set each factor equal to zero and solve for x:
   1. x + 16 = 0, so x = -16.
   2. x - 10 = 0, so x = 10.

Since we are looking for a length, the value of x must be positive. Therefore, the length of the garden is 10 feet. The width of the garden is x + 6 = 10 + 6 = 16 feet.

So, the dimensions of the garden are: Length 10 feet, Width 16 feet.