Question

If the perimeter of a rectangle is expressed by 6x^2 + 6x + 12 and the width is 2x^2 + 1, find an expression for the length.

Answer 1

The perimeter of a rectangle of width W and length L is given by:

`P=2(W+L)`

We have the expressions:

`\begin{gathered} P=6x^2+6x+12 \\ W=2x^2+1 \end{gathered}`

Then:

`\begin{gathered} (P)/(2)=W+L \\ \\ L=(P)/(2)-W \end{gathered}`

Using the expressions for P and W:

`\begin{gathered} L=(6x^2+6x+12)/(2)-2x^2-1=3x^2+3x+6-2x^2-1 \\ \\ \therefore L=x^2+3x+5 \end{gathered}`