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. 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)
○3.33
4.3 ft
1 ft
30 ft
Let's call the width of the metal piece w.
We are given that the area of the piece is 30 ft and can also be represented as length * width. So we can write this as:
w * (3w - 1) = 30
Expanding this:
3w^2 - w = 30
3w^2 - w - 30 = 0
Now, we can solve this quadratic equation to find the width of the metal piece:
w = (-(-1) ± sqrt((-1)^2 - 4 * 3 * -30)) / (2 * 3)
w = (1 ± sqrt(1 + 360)) / 6
w = (1 ± sqrt(361)) / 6
w = (1 ± 19) / 6
w = (1 + 19) / 6 = 20 / 6 = 3.33
w = (1 - 19) / 6 = -18 / 6 = -3 (disregard because width cannot be negative)
Therefore, the width of the metal piece should be approximately 3.33 ft rounded to the nearest hundredth of a foot.