SOLUTION: Help I've forgotton my math! I have a rectangle 9.75" X 6.5" whose area I need to increase by 11%. How do I figure this increase such that I will end up with the measurements fo

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Question 253476: Help I've forgotton my math!
I have a rectangle 9.75" X 6.5" whose area I need to increase by 11%. How do I figure this increase such that I will end up with the measurements for the sides of the new larger rectangle?

Found 3 solutions by Greenfinch, vksarvepalli, ankor@dixie-net.com:
Answer by Greenfinch(383)   (Show Source):
You can put this solution on YOUR website!
Multiply by the the square root of the increase sqrt(1.11)
9.75 x sqrt 1.11 = 10.272 "
6.5 x sqrt 1.11 = 6.85"

Answer by vksarvepalli(154)   (Show Source):
You can put this solution on YOUR website!
you have the present area = 63.375
the new area is 11% more= 1.11*63.375 = 70.34625
now you can increase the length or the breadth or both to get the area required
lets increase the length so the new length is n and breadth is same
now n*6.5=70.34625
so n=10.8225 is the new length

if we increase the breadth and keep length constant
let new breadth be m
now 9.75*m=70.34625
so m=7.215 is the new breadth

Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
I have a rectangle 9.75" X 6.5" whose area I need to increase by 11%.
How do I figure this increase such that I will end up with the measurements for the sides of the new larger rectangle?
:
Find the area you have now: 9.75 * 6.5 = 63.375
Find the increased area: 1.11 * 63.75 = 70.34625
:
Increase each dimension by x
(x + 9.75)*(x + 6.5) = 70.34625
FOIL
x^2 + 6.5x + 9.75x + 63.375 = 70.34625
x^2 + 16.25x + 63.75 - 70.34625 = 0
:
A quadratic equation
x^2 + 16.25x - 6.97125 = 0
:
Solve for x using the quadratic formula:
x = .41823 ~ .42 inches, add to each dimension (10.17 by 6.92)
;
:
Check this: 10.17 * 6.92 ~ 70.4