The area of a rectangule is (2x^2-11x+5). If the length is (2x-1), find the width.
w = A/L
w = (2 x^2 - 11 x + 5)/(2 x - 1)
= (2x-1)(x-5) / (2x-1)
= x-5
To find the width of a rectangle when given the area and length, you need to divide the area by the length. In this case, the area of the rectangle is given as (2x^2 - 11x + 5) and the length is (2x - 1).
To find the width, we can set up the equation:
Area = Length × Width
Substituting the given values:
(2x^2 - 11x + 5) = (2x - 1) × Width
To isolate the Width, we need to divide both sides of the equation by (2x - 1):
Width = (2x^2 - 11x + 5) / (2x - 1)
Now, in order to simplify the expression, we need to perform polynomial division. Let's divide (2x^2 - 11x + 5) by (2x - 1):
x - 2
___________________________
2x - 1 | 2x^2 - 11x + 5
- (2x^2 - x)
________________
-10x + 5
- (-10x + 5)
________________
0
The result of the division is (x - 2), which represents the width of the rectangle.
Therefore, the width of the rectangle is (x - 2).