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
The area of a rectangle can be calculated by multiplying the length by the width. In this case, we know the area is 30 ft² and the length is 1 less than 3 times the width.
Let's denote the width as w and the length as 3w - 1.
The area of the rectangle can be expressed as:
30 = w(3w - 1)
Expanding:
30 = 3w^2 - w
Rearranging to form a quadratic equation:
3w^2 - w - 30 = 0
Now we can use the quadratic formula to solve for w:
w = [-(-1) ± √((-1)^2 - 4*3*(-30))]/(2*3)
w = (1 ± √(1 + 360))/6
w = (1 ± √361)/6
w = (1 ± 19)/6
This gives two possible values for the width:
w = (1 + 19)/6 = 20/6 = 3.33 ft (rounded to the nearest hundredth)
So, the width of the metal piece should be 3.33 ft.