Diagonals AC and BD of rectangle ABCD intersect at point O, AO = 12.5, and AB: BC = 7: 24. Find the CD.

The diagonals of the rectangle at the intersection point are halved:
AC = 2 * AO = 2 * 12.5 = 25.
Consider a right-angled triangle ABC.
Let us introduce the proportionality coefficient k, then AB = 7k, BC = 24k.
Let’s use the Pythagorean theorem and write:
AC² = AB² + BC²
25² = (7k) ² + (24k) ²
625 = 49k² + 576k²
625 = 625k²
k² = 1
k = 1
CD = AB = 7k = 7 * 1 = 7
Answer: CD = 7