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^2. 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.

Answer 1

Let's denote the width of the metal piece as x (in feet). Then, the length of the metal piece would be (3x - 1) feet.

Since the area of the piece is 30 ft^2, we can set up the following equation:

Area = Length x Width
30 = (3x - 1) x

Expanding the right side of the equation, we get:

30 = 3x^2 - x

Rearranging the equation into standard form:

3x^2 - x - 30 = 0

Now, we can solve this quadratic equation for x using the quadratic formula:

x = [-(-1) ± √((-1)^2 - 4(3)(-30))] / 2(3)
x = [1 ± √(1 + 360)] / 6
x = [1 ± √361] / 6
x = [1 ± 19] / 6

Now, we have two possible values for the width of the metal piece:

1) x = (1 + 19) / 6 = 20 / 6 ≈ 3.33 feet
2) x = (1 - 19) / 6 = -18 / 6 = -3 feet

Since the width cannot be negative, the width of the metal piece should be approximately 3.33 feet when rounded to the nearest hundredth.