Question

Which one of the following formulas defines the area, A A , of a square in terms of its perimeter, p ?

Answer 1

A square has 4 sides of equa length

the perimiter is 4 times the side, or P=4s where s=length of 1 side

the area is length times witdth, but since the length=width, area=s² where s is the length of one side

so express A=s² in terms of P when P=4s

solve for s first in P=4s
P=4s
divide both sides by 4
$\frac{P}{4}=s$

subsitute $\frac{P}{4}$ for s in the other eqaution
$A=s^2$
$A=(\frac{P}{4})^2$
$A=\frac{P^2}{16}$



in terms of the perimiter, the area is $A=\frac{P^2}{16}$