Question 854764
We are given "A rope is square root 50 units long", so the rope is 5*sqrt(2) units long.
let x be one length and y is the other, we know
x + y = 5*sqrt(2)
x/y = 2/3
solve second equation for x
x = 2y/3
substitute for x in first equation
2y/3 +y = 5*sqrt(2)
multiply both sides of = by 3
2y +3y = 15*sqrt(2)
5y = 15*sqrt(2)
y = 3*sqrt(2)
x = 2 * 3*sqrt(2) / 3 = 2*sqrt(2)