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

`(P)/(4)=s`

subsitute
`(P)/(4)` for s in the other eqaution

`A=s^2`

`A=((P)/(4))^2`

`A=(P^2)/(16)`



in terms of the perimiter, the area is
`A=(P^2)/(16)`