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.
Let's denote the width of the metal piece as w and the length as 3w - 1.
The formula for the area of a rectangle is A = length * width.
Given that the area is 30 ft² and the length is 3w - 1, we have:
30 = (3w - 1) * w
30 = 3w² - w
3w² - w - 30 = 0
Now, we can solve the quadratic equation to find the value of w:
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 = 20 / 6 = 3.33 ft
Therefore, the width of the metal piece should be approximately 3.33 feet wide.