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 ft². 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)
Responses

3.33 ft
3.33 ft

4.3 ft
4.3 ft

1 ft
1 ft

30 ft
To find the width of the metal piece, we can set up the equation using the given information:
Let the width be w. The length is 3w - 1.
The area of a rectangle is length multiplied by width, so we have:
w(3w - 1) = 30
3w^2 - w = 30
3w^2 - w - 30 = 0
Now, we can solve for w using the quadratic formula:
w = (-[-1] ± √((-1)^2 - 4(3)(-30))) / 2(3)
w = (1 ± √(1 + 360)) / 6
w = (1 ± √361) / 6
w = (1 ± 19) / 6
w = (1 + 19) / 6 or w = (1 - 19) / 6
w = 20 / 6 or w = -18 / 6
w ≈ 3.33 ft
Therefore, the width of the metal piece should be approximately 3.33 ft.