A rectangular garden covers 16,000 ft2. Its length is 60 ft longer than its width.
What is the width of the garden?
100
width --- x
length ----x+60
x(x+60) = 16000
x^2 + 60x = 16000
completing the square is easy here
x^2 + 60x + 900 = 900+16000
(x+30)^2 = 16900
take √
x+30 = 130
x = 100
width is 100 ft, length is 160 ft
To find the width of the garden, we can set up an equation based on the given information.
Let's assume the width of the garden is "x" ft.
According to the problem, the length of the garden is 60 ft longer than the width. So, the length would be "x + 60" ft.
The formula for the area of a rectangle is Length × Width. We know that the area of the garden is 16,000 ft². So, we can set up the equation:
x(x + 60) = 16,000 ft²
To solve this equation, we can first simplify it:
x² + 60x = 16,000 ft²
Rearrange the equation to make it quadratic:
x² + 60x - 16,000 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or using the quadratic formula. In this case, factoring might be a bit tricky, so let's use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In our equation, a = 1, b = 60, and c = -16,000. Substituting these values into the quadratic formula:
x = (-60 ± √(60² - 4(1)(-16,000))) / (2(1))
Now, we can calculate the values inside the square root:
x = (-60 ± √(3,600 + 64,000)) / 2
x = (-60 ± √67,600) / 2
Taking the square root:
x = (-60 ± 260) / 2
Now, we have two possible answers for the width:
x₁ = (-60 + 260) / 2 = 200 / 2 = 100 ft
x₂ = (-60 - 260) / 2 = -320 / 2 = -160 ft
Since the width of a garden cannot be negative, we discard the second solution.
Therefore, the width of the garden is 100 ft.