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

September 30, 2021 | education

| 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.