find the range of possible side lengths that satisfy these conditions

Question

Use decimal form for numerical values

the perimeter of a square must be greater than 162 inches but less than 190 inches. find the range of possible side lengths that satisfy these conditions using interval notation

Answer 1

162 < x^2 < 190

sqrt(162) = sqrt(2*81) = 9 * Sqrt(2)

sqrt(190) = sqrt(10*19) = sqrt( 2* 5 * 19)

The exact answer is 9 * sqrt(2) < x < sqrt(2) * sqrt(5) * sqrt(19)

The approximate answer is

(12.727922061357855439215198517887‬, 13.784048752090221767955912552934‬)