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
Let's assume the width of the metal piece is x ft.
According to the given information, the length is 3x-1 ft.
The area of a rectangle is given by the formula: Area = length * width.
So, we can write the equation: 30 = (3x-1) * x.
Expanding the equation, we get: 30 = 3x^2 - x.
Rearranging the equation, we get: 3x^2 - x - 30 = 0.
To solve this quadratic equation, we can factorize or use the quadratic formula. Factoring is not possible easily, so let's use the quadratic formula.
The quadratic formula is given by: x = (-b ± sqrt(b^2 - 4ac)) / 2a.
For this equation, the values are: a = 3, b = -1, c = -30.
Substituting these values in the quadratic formula, we get: x = (-(-1) ± sqrt((-1)^2 - 4(3)(-30))) / (2)(3).
Simplifying the expression, we get: x = (1 ± sqrt(1 + 360)) / 6.
Calculating further, we get: x = (1 ± sqrt(361)) / 6.
The square root of 361 is 19.
So, we have two possible values for x: (1 + 19)/6 and (1 - 19)/6.
Simplifying these expressions further, we get: x = 20/6 and x = -18/6.
The value of x cannot be negative in this context, so we only consider the positive value.
Calculating further, we get: x = 10/3 = 3.33 ft (rounded to the nearest hundredth of a foot).
Therefore, the width of the metal piece should be approximately 3.33 ft.