In the triangle ABC, BK height, AB = 13, BC = 15, KC = 9. Find the area of the triangle ABC.

1. The ВСK triangle is rectangular, since the ВK is height. Using the formula of the Pythagorean theorem,

calculate its length:

ВK = √BC ^ 2 – KС ^ 2 = √15 ^ 2 – 9 ^ 2 = √225 – 81 = √144 = 12 units.

2. We calculate the length of the segment AK, also using the formula of the Pythagorean theorem:

AK = √AB ^ 2 – ВK ^ 2 = √13 ^ 2 – 12 ^ 2 = √169 – 144 = √25 = 5 units.

3. The length of the base AC of the triangle ABC is equal to AK + CK = 5 + 9 = 14 units.

4. The area of the triangle ABC = AC x ВK: 2 = 14 x 12: 2 = 84 units ^ 2.