8 of 88 of 8 Items Question 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 30 ft Skip to navigation
To solve this problem, we need to set up an equation based on the given information.
Let the width of the metal piece be x feet.
Given that the length is 1 less than 3 times the width, we can write the length as 3x - 1.
The area of a rectangle is given by the formula: Area = Length * Width
Given that the area of the metal piece is 30 ft², we can set up the equation:
30 = (3x - 1) * x
Now, solve for x by multiplying and simplifying:
30 = 3x^2 - x
Rearrange the equation:
3x^2 - x - 30 = 0
This is a quadratic equation that can be solved using the quadratic formula. The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 3, b = -1, and c = -30. Plug these values into the quadratic formula and solve for x to find the width of the metal piece.
x = (-(-1) ± √((-1)^2 - 4*3*(-30))) / 2*3
x = (1 ± √(1 + 360)) / 6
x = (1 ± √361) / 6
x = (1 ± 19) / 6
Since we are looking for the width, we take the positive value:
x = (1 + 19) / 6
x = 20 / 6
x = 3.33 ft (rounded to the nearest hundredth)
Therefore, the metal piece should be 3.33 feet wide.