The side of the triangle is split in a 2: 3 ratio and the division points are connected to the opposite apex of the triangle.

The side of the triangle is split in a 2: 3 ratio and the division points are connected to the opposite apex of the triangle. Find the ratio of the areas of the triangles into which the original triangle was divided.

Let point D divide the AC side, then CD = 2 * X cm, AD = 3 * X cm.

Let’s build the height BH of the triangle ABC to the base of the AC.

In triangle ABD and in triangle BCD BH there is also their height, drawn to the bases AD and CD.

Then Savd = AD * H / 2 = 3 * X * BH / 2.

Svsd = CD * BN / 2 = 2 * X * BN / 2.

Svsd / Savd = (2 * X * BH / 2) / (3 * X * BH / 2) = 2/3.

Answer: The area ratio is 2/3.