Geometry: the width and area of a rectangle
Is (4b^3+5b-3)/(2b-1)
What is the length of the rectangle?
Show work.
well, since 4b^3+5b-3 = (2b-1)(2b^2+b+3), I think it's clear...
Yes it is, thanks.
To find the length of a rectangle given the width and area, we need to use the formula for the area of a rectangle:
Area = Length × Width
In this case, the width is given as (4b^3 + 5b - 3) / (2b - 1), and the area is not provided. So, we need to find the area first, then solve for the length.
Since both the width and the area are expressed in terms of 'b', we can substitute the width formula into the area formula:
Area = Length × [(4b^3 + 5b - 3) / (2b - 1)]
Now, let's simplify the expression by multiplying the Length by the numerator:
Area = (Length × 4b^3 + Length × 5b - Length × 3) / (2b - 1)
To further simplify, we can distribute the Length to each term in the numerator:
Area = (4b^3 × Length + 5b × Length - 3 × Length) / (2b - 1)
Now, since we don't know the value of the area, we can't directly solve for the length. However, we have an essential piece of information: the width and length of a rectangle are perpendicular, which means the area is the product of the width and length.
Let's set up an equation using this information:
Length × Width = (4b^3 + 5b - 3) / (2b - 1)
Since we now have an equation involving the width and length, we can solve for either one using algebraic methods. However, without the specific value of the area given, we can't determine the precise length of the rectangle.