Question 168375
x^2=2/3(x+2)^2
x^2=2/3(x^2+4x+4)
x^2=(2x^2+8x+8)/3
3x^2=2x^2+8x+8
3x^2-2x^2-8x-8=0
x^2-8x-8=0
using the quadratic eqation{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}we get:
x=(8+-sqrt[-8^2-4*1*-8])/2*1
x=(8+-sqrt[64+32]) /2
x=(8+-sqrt96)/2
x=(8+-9.7979589)/2
x=(8+9.7979589)/2
x=17.7979589/2
x=8.898979 ans. for the length of the side of the picture.
Proof:
8.898979^2=2/3(10.898979)^2
79.19182=2/3*118.78774
79.19182=79.19182