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

Answer 1

The area of a rectangle is given by the formula: Area = length x width

Given that the area is 30 ft² and the length is 1 less than 3 times the width, we can set up the following equations:

1) Area = length x width
30 = (3w-1)w

2) Length = 3w-1

Now, we can substitute the expression for length from equation 2 into equation 1:

30 = (3w-1)w
30 = 3w² - w
3w² - w - 30 = 0

Now, we can solve for the value of w using the quadratic formula:

w = (-(-1) ± √((-1)² - 4(3)(-30))) / 2(3)
w = (1 ± √(1 + 360)) / 6
w = (1 ± √361) / 6
w = (1 ± 19) / 6

Therefore, the possible values for the width are:

w = (1 + 19) / 6 = 20 / 6 ≈ 3.33 ft
w = (1 - 19) / 6 = -18 / 6 = -3 (rejected due to being negative)

Therefore, the width of the metal piece should be approximately 3.33 ft.