Question

Which is a counterexample for the conditional statement?

If a square has side length s, then the perimeter is less than the area.

s = 3
s = 5
s = 7
s = 9

Answer 1

Perimeter P = 4s, area A = s^2. The statement requires 4s < s^2, i.e. s^2 − 4s > 0 → s(s − 4) > 0, which fails for 0 < s ≤ 4.

For s = 3: P = 12, A = 9, and 12 < 9 is false, so s = 3 is a counterexample. (s = 5, 7, 9 satisfy the inequality.)