Question

The area of the rectangle is given by the polynomial function A(x) = 6x^2 + 4x. If the width of the rectangle is 2x, what is the length?

Answer 1

Step 1: Write the formula for the area of a rectangle

`\text{Area of a rectangle = Length }*\text{ Width}`

Ste 2: Given data

`\begin{gathered} \text{Area of a rectangle = 6x}^2\text{ + 4x} \\ \text{Width = 2x} \\ \text{Length = ?} \end{gathered}`

Step 3: Substitute the values in the area formula to find the length.

`\begin{gathered} \text{Area of a rectangle = Length }*\text{ Breadth} \\ Length\text{ of a rectangle = }\frac{Area\text{ of a rectangle}}{\text{Width}} \\ Length\text{ = }\frac{6x^2\text{ + 4x}}{2x} \\ \text{Length = }(6x^2)/(2x)\text{ + }(4x)/(2x) \\ \text{Length = 3x + 2} \end{gathered}`

Step 4: Final answer

`\text{Length = 3x + 2}`