In right-angled triangle ABC, the height CD is dropped from the vertex of the right angle C.

In right-angled triangle ABC, the height CD is dropped from the vertex of the right angle C. Find its hypotenuse AB, if AC = 10 cm, AD = 4 cm.

1. Since CD is height, another triangle ADC is formed, right angle D.

2. Consider triangles ABC and ADC, they are rectangular, and have a common angle. This means that these triangles are similar (by the first sign of similarity of right-angled triangles), and their sides are proportional.

3. Find the hypotenuse AB.

Let’s make a proportion

AC / AB = AD / AC; Let us express AB

AB = (AC * AC) / AD;

AB = (10 * 10) / 4 = 25 (cm) the sought hypotenuse of the triangle ABC.

Answer: 25 cm.