In a right-angled triangle ABC (angle C = 90 *), we draw the height CD. Find the segment BD if AB = 8cm, BC = 4cm

Given:
Right-angled triangle ABC
angle C = 90 degrees
СD – height,
BC = 4 cm
AB = 8 cm
Find the length of the segment BD -?
Solution:
Consider a right-angled triangle ABC.
In a right-angled triangle, each leg is the average proportional between the hypotenuse and the projection of this leg onto the hypotenuse.
Then BC = √ (AB * DB). By the condition of the problem BC = 4 cm and AB = 8 cm, then
4 = √ (8 * DB) (let’s square the right and left parts);
16 = 8 * DB;
DB = 16: 8;
DB = 2 centimeters – the length of the segment DB.
Answer: 2 centimeters.