Question

A rectangle has a perimeter equal to 24. Ifwe consider its width x, how could wetalk about its length y in terms of x?What are possible values of x? What arepossible values of y? y= length =width =

Answer 1

The perimeter of a rectangle is given by:

$\begin{gathered} P=2(L+W) \\ L\text{ is the Length} \\ W\text{ is the Width} \end{gathered}$

We are provided with the following:

$P=24,\text{ L=y, W=x}$

We could talk about its length y in terms of x, as shown below:

$\begin{gathered} P=2(L+W) \\ 24=2(y+x) \\ \frac{24}{2}=y+x \\ 12=y+x \\ 12-x=y \\ \text{Therefore, y=12-x} \end{gathered}$

The possibles values of x are:

$x=5\text{ or x=4}$

The possible values of y are:

$\begin{gathered} y=12-x \\ \text{when x=5} \\ y=12-5 \\ y=7 \end{gathered}$$\begin{gathered} \text{When x=4} \\ y=12-4 \\ y=8 \end{gathered}$