help!! area issues?

Question

Matt's rectangular patio measures 9 feet by 12 feet. He wants to increase the patio's dimensions so its area will be twice the area it is now. He plans to increase both the length and the width by the same amount, x. Find x?

Note: i found the area for the original patio =108 and doubled that = 216 but then i divided 216 by 108 and got 2 doesnt really seem right. Help

Answer 1

Length* Width = Area

9*12 = 108 , original patio
double the area = 216
new length = 9+x, new width = 12 +x
so
(9+x) * (12+x) = 216
so x = 4.2733

Answer 2

9*12=108
(9+x)*(12+x)=216
108+21x+x^2=216
x^2+21x+108=216
x^2+21x+108-216=0
x^2+21x-108=0

(-b+-sqr(b^2-4ac))/2a
a=1; b=21; c=-108

(-21+-sqr((21)^2-4*1*-216)/2
(-21+-sqr(441+864))/2
(-21+-sqr(1305))/2
(-21+-sqr(145*9))/2
(-21+-(3*sqr(145))/2

-(3*sqr(145)/2) is aprroximately 18.062

-21+18.62 = negative number
-21-18.62=negative number

so there is no solution where you can increase the sides and make the square double

this is actually a famous math problem ... and there is no solution

Answer 3

108*2=216 so this is his projected area.

and both dimensions are x so x*x will get you 216

a=l*w
216=x*x
216=x^2
216(sqrd)=x(sqrd)
x=14.69

ok so the dimensions could be 14.69 by 14.69 but i didn't increase both by the same amount...

anyway if u checked

a=l X W
216=14.69 X 14.69
216=216

Left side equals right side