Question

The perimeter of a square I must be greater than 102 inches but less than 138 inches find the range of the possible side lengths that satisfy these conditions hit the perimeter of the square is given by P equals 4S or S represent the length of the side explain your answer in interval notation used decimal forms for numerical value

Answer 1

The Solution:

Given:

$\begin{gathered} 102

We are required to find the range of a side (s).

[tex]102<4s\text{ or }4s<138$

So,

$\begin{gathered} 102<4s \\ \\ 4s>102 \\ \\ s>\frac{102}{4} \\ \\ s>\frac{51}{2} \\ \\ s>25.5 \end{gathered}$

Similarly,

$\begin{gathered} 4s<138 \\ \\ s<\frac{138}{4} \\ \\ s<\frac{69}{2} \\ \\ s<34.5 \end{gathered}$

Therefore, the correct answer is (25.5, 34.5)