In a triangle CDE, CD = 15 cm, DE = 13 cm, CE = 14 cm. Find the height DM.

Let’s calculate what the value of the half-perimeter of this triangle is equal to, if all its sides are known:

(15 + 14 + 13): 2 = 21.

Let’s calculate what the value of the area of this geometric figure will correspond to, using the formula, which is known as Heron’s formula:

√21 (21 – 15) (21 – 14) (21 – 13) = √7056 = 84.

Let’s calculate what the height DM will be, using the definition that the area of a triangle is half the product of the height and the base:

14 * x / 2 = 84;

x = 12.

Answer: DM is 12 centimeters.