In a right-angled triangle ABC, angle C = 90 degrees AC = 6cm, AB = 9cm SD-height. Find the VD.

Given:
right triangle ABC
angle C = 90 degrees
SD – height
AC = 6 cm
AB = 9 cm
Find VD -?
Decision:
1) In a right-angled triangle, each leg is the average proportional between the hypotenuse and the projection of this leg onto the hypotenuse. Then AC = √ (AB * HELL). By the condition of the problem AC = 6 cm and AB = 9 cm, then
6 = √ (9 * HELL) (square the right and left parts);
36 = 9 * HELL;
BP = 36: 9;
BP = 4 centimeters:
2) VD = AB – HELL;
VD = 9 – 4;
VD = 5 centimeters.
Answer: 5 centimeters.