Question

The perimeter of a square must be greater than 162162 inches but less than 190190 inches. find the range of possible side lengths that satisfy these conditions. (hint: the perimeter of a square is given by p=4sp=4s, where s represents the length of a side).

Answer 1

Since the perimeter is four times the side, the constraints on the perimeter are immediately translated into constraints on the side:

$162 < p < 190 \iff 162 < 4s < 190$

So, if you divide every term in the inequality by 4, you have

$\dfrac{162}{4} < s < \dfrac{190}{4}$

Now simply evaluate the fractions:

$40.5 < s < 47.5$