The sides of the triangle are in the ratio 3: 4: 6. Combining the midpoints of all sides, we get a triangle

| September 17, 2021 | education

The sides of the triangle are in the ratio 3: 4: 6. Combining the midpoints of all sides, we get a triangle with a perimeter of 5.2 m. Find the sides of this triangle ..

Let the length of the segment AC = 3 * X cm, the length of the segment AB = 4 * X cm, the length of the segment BC = 6 * X cm.

Points K, M, H are the midpoints of the sides of the triangle ABC, then the segments KM, KN, MN are the midlines of the triangle ABC,

Then KM = AC / 2 = 3 * X / 2 = 1.5 * X cm, KN = BC / 2 = 6 * X / 2 = 3 * X cm, MH = AB / 2 = 4 * X / 2 = 2 * X cm.

Then Rkmn = 1.5 * X + 3 * X + 2 * X = 5.2 cm.

6.5 * X = 5.2.

X = 5.2 / 6.5 = 0.8.

Then AB = 4 * 0.8 = 3.2 cm, BC = 6 * 0.8 = 4.8 cm, AC = 3 * 0.8 = 2.4 cm.

Answer: The sides of the triangle are 2.4 cm, 3.2 cm, 4.8 cm.



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