Question

Given the perimeter of a rectangle and either the length or width, find the unknown measurement using the appropriate formula.The perimeter is 12mm and the width is 2mm the length of the rectangle is what?

Answer 1

To calculate the perimeter of a rectangle you have to add all of its sides, that is

$P=w+w+l+l$

You can simplify it as:

$P=2w+2l$

If you know the perimeter and width of a rectangle, you can calculate the length.

First write the formula in terms of the length:

$\begin{gathered} P-2w=2l \\ l=\frac{P-2w}{2} \\ l=\frac{P}{2}-\frac{w}{2} \\ l=\frac{P}{2}-w \end{gathered}$

For P=12mm and w=2mm

$\begin{gathered} l=\frac{P}{2}-w \\ l=\frac{12}{2}-2 \\ l=4 \end{gathered}$

The length of a rectangle with perimeter of 12mm and width of 2mm is 4mm