Explanation:

To find the length of the chord in the circle:

- The radius of the circle is given as 13 cm.

- The distance from the center to the chord (perpendicular) is 5 cm.

- Using the Pythagorean theorem in the right triangle formed by the radius, the distance from the center to the chord, and half the chord's length:

- Let half of the chord's length be \( x \).

- The equation is: \( x^2 + 5^2 = 13^2 \).

- Solve for \( x \): \( x^2 + 25 = 169 \).

- \( x^2 = 144 \).

- \( x = 12 \).

- Therefore, the full length of the chord is \( 2 \times x = 24 \) cm.

- Option 1: 24 cm is the correct choice.