The perimeter of the square is to be from 16 meters to 36 meters.Find the range of values for its area S.
A) $\quad 64

Question

The perimeter of the square is to be from 16 meters to 36 meters.Find the range of values for its area S. 
A) $\quad 64 < S < 324$
B) $\quad 16 < S < 81$
C) $\quad 4 < S < 9$
D) $\quad 256 < S < 1296$
E) none of the above

Quizplus · Accepted Answer

Let the side of the square be $s$. Then we have $16 \leq 4s \leq 36$, which simplifies to $4 \leq s \leq 9$.

The area of the square is $s^2$, so when $s=4$, we get $S=16$, and when $s=9$, we get $S=81$. Therefore, the range of values for $S$ is $16 \leq S \leq 81$.

Option $	extbf{(B)}$ gives this range, so it is the correct answer.

The Perimeter of the Square Is to Be from 16 64<S<324\quad 64 < S < 32464<S<324

The Perimeter of the Square Is to Be from 16 $\quad 64 < S < 324$