In triangle ABC, segment CD is the height corresponding to side AB, and AE

In triangle ABC, segment CD is the height corresponding to side AB, and AE is the height corresponding to side BC. Find CD if AB = 10 cm, AE = 6 cm, BC = 12 cm.

By condition, we have the length of two bases AB and BC of the triangle, and the heights AE and CD drawn to these bases, the length of one of which is not known.

Let us express the area of the triangle ABC in two ways, and then equate them.

S = AB * CD / 2 = 10 * CD / 2 = 5 * CD.

S = BC * AE / 2 = 12 * 6/2 = 36 cm.

5 * CD = 36

CD = 36/5 = 7.2 cm

Answer: Height СD = 7.2 cm.