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?

Question

3 /10 units
10 /5 units
10/2 units
2/10 units
Where / means square root

Answer 1

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