Question

A rope is \sqrt(250)units long. The rope is cut into two pieces, so the length of the pieces are in a ration of 3:2. What is the length of the longer piece expressed in simple radical form?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let the length of the longer piece be 3x units. Then the length of the shorter piece is 2x units.

According to the given information, we have:

3x + 2x = \sqrt(250)
5x = \sqrt(250)
x = \frac{\sqrt(250)}{5}
x = \sqrt(10)

Therefore, the length of the longer piece is 3x = 3 * \sqrt(10) = \sqrt(100) = 10 units.

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

Let the longer piece of the rope be 3x units long and the shorter piece be 2x units long.

According to the information given, we have:
3x + 2x = \sqrt{250}
5x = \sqrt{250}
x = \frac{\sqrt{250}}{5}
x = \frac{\sqrt{2}\sqrt{125}}{5}
x = \frac{5\sqrt{2}}{5}
x = \sqrt{2}

Therefore, the length of the longer piece is 3x = 3\sqrt{2} or 3\sqrt{2} units long.