Question

A rope is the square root of 75 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?

A. 2√3 units
B. 3√5 units
C. 3√2 units
D. 3√3 units"

Answer 1

The length of the longer piece of rope cut in the ratio of 2:3 from a rope of √75 units is 3√5 units.

Step-by-step explanation:

The length of a rope is the square root of 75 units, which can be written as √75 units. This rope is cut into two pieces with lengths in the ratio of 2:3. To find the length of the longer piece in simplest radical form, we need to express √75 using its prime factors. √75 is equivalent to √(3² × 5), which simplifies to 3√5. Since the ratio of the lengths is 2:3, and the total length is 3√5, we divide this by the sum of the ratio parts (2+3=5) and then multiply by the larger ratio number (3) to find the length of the longer piece. This yields (3√5 ÷ 5) × 3 = (√5 × 3).

Therefore, the length of the longer piece is 3√5 units.