Point K is marked in triangle ABC on its median BM so that BK: KM = 7: 3. Find the ratio of the area

univerkov | May 24, 2021 | education

Point K is marked in triangle ABC on its median BM so that BK: KM = 7: 3. Find the ratio of the area of triangle ABK to the area of triangle ABC.

Since BM is the median of triangle ABC, it divides it into two equal triangles.

Savm = Svcm = Savs / 2 cm2.

The area of the triangle ABM is equal to: Sawm = Sawk + Samk.

The triangles ABK and ABK have a total height AH, when the ratio of the areas of these triangles is equal to the ratio of their bases.

Sawk / Samk = 7/3.

Sam = 3 * Sav / 7.

Then Sawm = Sawc / 2 = Sawk + 3 * Sawk / 7 = 10 * Sawk / 7.

Savk / Savs = 7/20.

Answer: The area ratio is 7/20.

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