SOLUTION: A rope is square root 50 units long. The rope is cut into two pieces, so that the lengths of the pieces are in the ratio 2:3. What is the length of the longer piece expressed in si

Question 854764: A rope is square root 50 units long. The rope is cut into two pieces, so that the lengths of the pieces are in the ratio 2:3. What is the length of the longer piece expressed in simplest radical form?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
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)
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