The sides of a triangle are in a ratio of 4: 3: 5. the perimeter of the triangle formed by the connection of all its midpoints

| February 17, 2021 | education

The sides of a triangle are in a ratio of 4: 3: 5. the perimeter of the triangle formed by the connection of all its midpoints of the sides is 3.6 dm. find the sides of a given triangle

The connection of the midpoints of the sides of a triangle is called the midline of the triangle. It is parallel to the third side, and its length is equal to half the length of this side. Therefore, it can be argued that the sides of the smaller triangle will also be related as 4: 3: 5.

Since the perimeter of the triangle formed by the middle lines is 3.6 dm, and the sides are related as 4: 3: 5, we will express it as follows (For convenience of calculation, we will translate all the values ​​into centimeters 1 dm = 10 cm):

4x – length of segment AB;

3x – the length of the BC segment;

5x – length of the AC segment;

4x + 3x + 5x = 36;

12x = 36;

x = 36/12 = 3;

AB = 4 3 = 12 cm;

BC = 3 3 = 9 cm;

AC = 5 3 = 15 cm.

Answer: the sides of the triangle formed by the middle lines are 12 cm = 1.2 dm, 9 cm = 0.9 dm, 15 cm = 1.5 dm.



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