The area of a rectangle is 30 ft^2. The length is 1 less then 3 times the width. How wide is is the rectangle?
thank you
Let's denote the width of the rectangle as "w" (in ft). According to the given information, the length is 1 less than 3 times the width, which can be expressed as (3w - 1).
The formula to calculate the area of a rectangle is given by:
Area = Length * Width
In this case, the area is given as 30 ft^2. Therefore, we have the equation:
30 = (3w - 1) * w
Now, let's solve this quadratic equation for w:
30 = 3w^2 - w
Rearranging the equation to standard quadratic form:
3w^2 - w - 30 = 0
Next, let's factorize this equation:
(3w + 10)(w - 3) = 0
Setting each factor equal to zero:
3w + 10 = 0 or w - 3 = 0
Solving each equation separately:
1) 3w + 10 = 0
3w = -10
w = -10/3
2) w - 3 = 0
w = 3
Since width cannot be negative in this context, we discard the solution w = -10/3.
Therefore, the width of the rectangle is 3 ft.
To find the width of the rectangle, we can set up an equation using the given information. Let's denote the width of the rectangle as 'w'.
According to the problem, the length of the rectangle is 1 less than 3 times the width. Therefore, the length can be expressed as (3w - 1).
The formula for the area of a rectangle is length multiplied by width. Given that the area is 30 ft^2, we can set up the following equation:
(3w - 1) * w = 30
Now, we can solve the equation to find the width of the rectangle.
L = 3w -1
Area = Lw
30 = (3w-1)w
30 = 3w^2 - w
3w^2 - w - 30 = 0
factor if not factor then
use quadratic formula