On the sides AB and AC of triangle ABC, the area of which is 50, points M and K are taken, respectively

On the sides AB and AC of triangle ABC, the area of which is 50, points M and K are taken, respectively, so that AM: MB = 1: 5, and AK: KC = 3: 2. What is the area of triangle AMK?

Side AB of triangle ABC consists of 6 parts, moreover, AM consists of one part, and MB – of two parts.

Side AC of triangle ABC consists of 5 parts, moreover, AK consists of three parts, and CK – of two parts.

The sides AM and AK enclose the triangle AMK, so we have: S △ AMK = (AM / AB) * (AK / AC) * S △ ABC = 1/6 * 3/5 * 50 = 5.

Answer: 5.