Question

The perimeter of a square must be greater than 122 inches but less than 134 inches. Find the range of possible side lengths that satisfy these conditions. Hint the perimeter of a square is given by p = 4s, where s represents the length of a side).

Answer 1

Let the perimiter of the square P

Statement 1

The perimeter of the square is greater than 122 inches

This can be expressed in inequality as

`P>122`

Statement 2

The perimeter of the square is less than 134 inches

This can be expressed in inequality as

`P<134`

Since P = 4S, hence

`4s>122,4s<134`

Solving for s gives

`\begin{gathered} 4s>122 \\ \Rightarrow s>(122)/(4) \\ \Rightarrow s>30.5 \end{gathered}`

Aslo

`\begin{gathered} 4s<134 \\ \Rightarrow s<(134)/(4) \\ \Rightarrow s<33.5 \end{gathered}`

Hence

`s>30.5,s<33.5`

Combining the inequalities gives

`30.5<p></p><p></p><p></p>[tex]\text{.}`