Question

13. The area of a rectangle is given by the expression 6x² + x - 1. If the width of the rectangle is 2 units, then interms of x , what is the simplified, expanded expression for the perimeter of this rectangle?

Answer 1

We have the following:

`\begin{gathered} A=w\cdot l \\ A=6x^(2)+x-1 \\ w=2 \end{gathered}`

to calculate the length:

`\begin{gathered} l=(A)/(w) \\ l=(6x^(2)+x-1)/(2) \\ l=(6x^2)/(2)+(x)/(2)-(1)/(2) \\ l=3x^2+(x)/(2)-(1)/(2) \end{gathered}`

the perimeter is:

`p=2\cdot w+2\cdot l`

replacing:

expanded expression:

`\begin{gathered} p=2\cdot2+2\cdot(3x^2+(x)/(2)-(1)/(2)) \\ p=4+2\cdot(3x^2+(x)/(2)-(1)/(2)) \end{gathered}`

simplifed expression:

`\begin{gathered} p=2\cdot2+2\cdot(3x^2+(x)/(2)-(1)/(2)) \\ p=4+2\cdot3\cdot x^2+2\cdot(x)/(2)-2\cdot(1)/(2) \\ p=4+6x^2+x-1 \\ p=6x^2+x+3 \end{gathered}`