The area of a rectangular floor is 72 ft2. The length of the floor is 1 ft more than 3 times the width. How wide is the floor (rounded to the nearest whole number)?
area = width * length
length = 1+3*width
area = width * (1+3*width)
72 = w(1+3w) = w + 3w2
3w2 + w - 72 = 0
w = (-1 + sqrt(865))/6 = 4.7
so, rounding up, w = 5'
To find the width of the floor, we need to set up an equation based on the given information.
Let's assume the width of the floor is "w" ft.
According to the given information, the length of the floor is 1 ft more than 3 times the width. So the length can be expressed as (3w + 1) ft.
The formula to find the area of a rectangle is:
Area = Length * Width
We can substitute the values into this formula:
72 = (3w + 1) * w
Now, let's solve this equation to find the width:
First, distribute the w to both terms inside the parentheses:
72 = 3w^2 + w
Rearrange the equation to set it equal to zero:
0 = 3w^2 + w - 72
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula.
In this case, let's solve it by factoring:
0 = (3w - 8)(w + 9)
Set each factor equal to zero and solve for w:
3w - 8 = 0 or w + 9 = 0
3w = 8 or w = -9
w = 8/3
Since we are looking for the width of the floor, we only consider the positive value of w. Rounding the value to the nearest whole number, the width of the floor is approximately 3 ft.