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

$\begin{gathered} 4s>122 \\ \Rightarrow s>\frac{122}{4} \\ \Rightarrow s>30.5 \end{gathered}$

Aslo

$\begin{gathered} 4s<134 \\ \Rightarrow s<\frac{134}{4} \\ \Rightarrow s<33.5 \end{gathered}$

Hence

$s>30.5,s<33.5$

Combining the inequalities gives

$30.5

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