In a right-angled triangle ABC with a right angle C, the middle line MN is drawn, parallel to the leg AC.

In a right-angled triangle ABC with a right angle C, the middle line MN is drawn, parallel to the leg AC. Find the length of the midline MN if AB = root of 136, BC = 10

1. Applying the Pythagorean theorem, we calculate the length of the AC leg:

AC ^ 2 = AB ^ 2 – BC ^ 2 = (√136) ^ 2 – 10 ^ 2 = 136 – 100 = 36;

AC = √36 = 6.

2. Using the property of the midline of the triangle that it is equal to half of the parallel

hand, we calculate the length МN:

MN = AC / 2 = 6/2 = 3 units.

Answer: the length of the middle line МN of the triangle ABC is equal to 3 units.