HisokaIsMyDad HisokaIsMyDad
  • 15-09-2020
  • Mathematics
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Which is a counterexample for the conditional statement? If a square has side length s, then the perimeter is less than the area.

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sqdancefan
sqdancefan sqdancefan
  • 15-09-2020

Answer:

  s = 3: perimeter 12, area 9

Step-by-step 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.

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