Sides AB and BC of triangle ABC are 16 cm and 22 cm, respectively, and the height drawn to side

Sides AB and BC of triangle ABC are 16 cm and 22 cm, respectively, and the height drawn to side AB is 11 cm. Find the height drawn to side BC.

The area of the triangle ABC is equal to

S = ½ * АB * h, where h is the height drawn to the side АB.

Find the area of the triangle:

S = ½ * 16 * 11 = 88 cm².

On the other hand, the area of this triangle is

S = ½ * BC * h1, where h1 is the height drawn to the BC side.

Let us express h1 from this formula:

h1 = 2S / BC.

Let’s find the height we need:

h1 = 2 * 88/22 = 8 cm.

Answer: The height drawn to side BC of triangle ABC is 8 cm.