Points P and Q are midpoints of sides AB and AC of triangle ABC. Find the perimeter of triangle ABC

Points P and Q are midpoints of sides AB and AC of triangle ABC. Find the perimeter of triangle ABC if the perimeter of triangle APQ is 21 cm.

Since, by catch, points P and Q are the midpoints of the sides AB and AC, then the segment PQ is the midline of the triangle ABC, then PQ is parallel to BC, PQ = BC / 2.

In triangles ABC and APQ, the angle at the vertex A is common, the angle ABC is equal to the angle APQ as the corresponding angles at the intersection of parallel lines BC and PQ secant AB, then triangle ABC is similar to triangle APQ.

The coefficient of similarity of triangles is: K = PQ / AB = 1/2.

The perimeters of such triangles are referred to as a coefficient of similarity.

Papq / Pavs = 1/2.

Ravs = 21 * 2 = 42 cm.

Answer: The perimeter of triangle ABC is 42 cm.