a flower garden has a length that is 4 feet shorter than twice it's width. The area of the garden is 96 square feet. What are the dimensions?
My answer ?.
To find the dimensions of the flower garden, we can set up an equation based on the information given.
Let's represent the width of the garden as "w."
According to the problem, the length of the garden is 4 feet shorter than twice its width, so the length would be 2w - 4.
The area of the garden is given as 96 square feet, so we can set up the equation:
Area = Length × Width
96 = (2w - 4) × w
Now, let's solve this equation to find the value of "w."
Step 1: Expand the equation:
96 = 2w² - 4w
Step 2: Rearrange the equation to make it a quadratic equation:
2w² - 4w - 96 = 0
Step 3: Simplify the equation by dividing through by 2:
w² - 2w - 48 = 0
Step 4: Factorize the quadratic equation:
(w - 8)(w + 6) = 0
Step 5: Solve for "w" by setting each factor equal to zero:
w - 8 = 0
w = 8
w + 6 = 0
w = -6 (discarding this solution because width cannot be negative)
Therefore, the width of the flower garden is 8 feet.
To find the length, we can substitute the value of "w" back into the expression 2w - 4:
Length = 2w - 4
Length = 2(8) - 4
Length = 16 - 4
Length = 12
Therefore, the length of the flower garden is 12 feet.
So, the dimensions of the flower garden are 8 feet (width) by 12 feet (length).
w(2w-4) = 96
now expand and solve the quadratic.
Note that two factors of 96 are 8 and 12.