The height drawn from the vertices of the right angle of a right-angled triangle divides the hypotenuse

The height drawn from the vertices of the right angle of a right-angled triangle divides the hypotenuse into segments equal to 25 cm and 7 cm. What is the height.

Let us prove that triangle ABC is similar to triangle BCD.

Both triangles are rectangular, ABC by condition, BCD since BD is height. Let the angle BAC = α, then the angle ABD = (90 – α), and the angle CDB = 90 – (90 – α) = α. Angle BAC = CBD, then right-angled triangles are similar in acute angle.

BC / CD = AD / BC.

BC ^ 2 = CD * AD = 7 * 25 = 175.

BC = 5 * √7 cm.

Answer: The height of the triangle is 5 * √7 cm.