Heights AK and BD are drawn in an acute-angled triangle ABC. It is known that AK = 4cm

Heights AK and BD are drawn in an acute-angled triangle ABC. It is known that AK = 4cm, BD = 8cm, KC = 3cm. Find the area of triangle ABC.

Since AK is the height of triangle ABC, then triangle ACK is rectangular, in which, by condition, CK = 3 cm, AK = 4 cm.Then, by the Pythagorean theorem, AC ^ 2 = AK ^ 2 + CK ^ 2 = 16 + 9 = 25 cm.

AC = 5 cm.

Then the area of the triangle ABC will be equal to:

Sас = ВD * АС / 2 = 8 * 5/2 = 20 cm2.

Answer: The area of the triangle ABC is 20 cm2.