A rope is /250 units long. The rope is cut into two pieces, so that the lengths of the pieces are in the ratio 3:2. What is the length of the longer piece expressed in simplest radical form?
3 /10 units
10 /5 units
10/2 units
2/10 units
Where / means square root
Let the lengths of the two pieces of rope be 3x and 2x, where x is a positive constant.
According to the given ratio, we have 3x + 2x = 250.
Combining like terms, we get 5x = 250.
Dividing both sides by 5, we have x = 50.
So, the lengths of the two pieces of rope are 3x = 3 * 50 = 150 units and 2x = 2 * 50 = 100 units.
The length of the longer piece is 150 units.
Therefore, the length of the longer piece expressed in simplest radical form is 10/√2 units. Answer: 10/√2 units