Question

Find the perimeter of a square if the length of one side is given. Are the perimeter of the square and the length of its side directly proportional quantities a=6

Answer 1

The perimeter of a polygon is the distance around it.

In the case of a square, since all its sides are equal, the perimeter is given by:

`\begin{gathered} P=a+a+a+a \\ P=4a \end{gathered}`

where a is the length of each side. Therefore the perimeter is:

`P=4a`

Two quantities are directly proportional if as one amount increases, another amount increases at the same rate. With this in mind we conclude that the perimeter of a square is proportional to its side length.

If a=6 then the perimter is:

`\begin{gathered} P=4(6) \\ P=24 \end{gathered}`

Therefore if the length is 6 the perimeter is 24.