One more rectangular-shaped piece of metal siding needs to be cut to cover the exterior of a pole barn. The area of the piece is 30 ft^2. The length is 1 less than 3 times the width. How wide should the metal piece be? round to the nearest hundredth of a foot.
(1 point)
A. 3.33 ft
B. 4.3 ft
C. 1 ft
D. 30 ft
Let's say the width of the metal piece is x ft. According to the given information, the length is 3x - 1 ft.
We know that the area of a rectangle is given by the formula: Area = Length × Width
So, we can write the equation: 30 ft^2 = (3x - 1 ft) × (x ft)
Now, we can solve this equation for x:
30 ft^2 = 3x^2 - x ft
3x^2 - x - 30 = 0
This equation does not factor easily, so we can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = 3, b = -1, and c = -30.
x = (-(-1) ± sqrt((-1)^2 - 4(3)(-30))) / (2(3))
x = (1 ± sqrt(1 + 360)) / 6
x = (1 ± sqrt(361)) / 6
x = (1 ± 19) / 6
We ignore the negative solution since width cannot be negative, so:
x = (1 + 19) / 6
x = 20/6
x ≈ 3.33 ft
Therefore, the width of the metal piece should be approximately 3.33 ft. Answer choice A.