Question 636347: If the perimeter of a square increases by 25% then its area increases by ? Found 3 solutions by sachi, solver91311, ptaylor:Answer by sachi(548) (Show Source):
You can put this solution on YOUR website! If the perimeter of a square increases by 25% then its area increases by ?
ans:=
let the sides be a =>perimeter=4a
new perimeter=4A=4a+4a*25%=4a(1.25)
so A=a(1.25)
now new area=A^2=a^2(1.25)^2=a^2*1.5625
so the % increase in area=(A^2-a^2)*100/a^2=a^2(0.5625)*100/a^2=56.25% ans
If you increase the perimeter of a square by 25%, you must increase each side by 25%, so now each side is 1.25 times the original measure. The area of the original square would be and the area of the new square is . Square 1.25 to get the factor of increase, subtract 1, then multiply by 100 to get the percentage increase.
John
My calculator said it, I believe it, that settles it
You can put this solution on YOUR website! Area of square=Side*Side or A=S^2---formula #1
Perimeter of square=Side+Side+Side+Side or P=4S or S=P/4 formula #2
Lets put the value of S from formula #2 into formula #1 and we get
A(b)=(P/4)^2=P^2/16-----formula #3-- before the increase
Now if we increase P by 25%, we get 1.25P
A(a)=(1.25P)^2/16=1.562P^2/16----formula #4---after increase
Looking at formula #4, we see that P^2/16=A(b); the area before the increase
Sooooo A(a)=1.56A(b) or the area after the perimeter is increased increases by 1.562 units
Hope this helps---ptaylor
