Question

Which is a counterexample for the conditional statement? If a square has side length s, then the perimeter is less than the area.

Answer 1

s = 3: perimeter 12, area 9

Explanation:

We are interested in side lengths s such that ...

P ≥ A

4s ≥ s²

4s -s² ≥ 0

s(4 -s) ≥ 0

This is the equation of a parabola that opens downward. I has zeros at s=0 and s=4, so will have a value at least 0 for 0 ≤ s ≤ 4.

A square of side length 3 will have a perimeter greater than the area.