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 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.
Answers
GPT 3.5
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.
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.