In a triangle, the sum of the two sides is 14 cm, and the third side is divided by the bisector of the opposite angle

| September 3, 2021 | education

In a triangle, the sum of the two sides is 14 cm, and the third side is divided by the bisector of the opposite angle into segments equal to 3 and 4 cm. Find the sides of the triangular.

Let ABC be a given triangle. BE – bisector of angle B. AE = 3 cm, CE = 4 cm.

Let’s calculate the length of the side of the speaker: 3 + 4 = 7 cm.

Let’s denote the side BC by the letter x, then AB = 14 – x (since the sum of AB and BC is 14 cm).

By the property of the angle bisector (the bisector divides the opposite side of the triangle into parts proportional to the adjacent sides), we get:

BC / CE = AB / AE;

x / 4 = (14 – x) / 3.

According to the rule of proportion:

3x = 4 (14 – x);

3x = 56 – 4x;

3x + 4x = 56;

7x = 56;

x = 56/7 = 8 (cm) – the length of the BC side.

AB = 14 – x = 14 – 8 = 6 (cm).

Answer: the sides of the triangle are 6 cm, 7 cm and 8 cm.



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