The sides of triangle ABC are 14 cm, 12 cm and 8 cm, and the vertices are the midpoints of the sides

The sides of triangle ABC are 14 cm, 12 cm and 8 cm, and the vertices are the midpoints of the sides of another triangle. Find the perimeter of the larger triangle.

If the midpoints of the sides of the triangle are connected by segments, then these segments will be the midlines of this triangle.

These lines are parallel to the third side and equal to half its length:

AB = A1B1 / 2;

BC = B1C1 / 2;

AC = A1C1 / 2.

Thus:

A1B1 = 2AB;

A1B1 = 2 14 = 28 cm;

B1C1 = 2BC;

B1C1 = 2 * 12 = 24 cm;

A1C1 = 2AC;

A1C1 = 2 * 8 = 16 cm.

The perimeter of a triangle is the sum of all its sides.

PA1B1C1 = A1B1 + B1C1 + A1C1;

PA1B1C1 = 28 + 24 + 16 = 68 cm.

Answer: The perimeter of the larger triangle is 68 cm.