The bisector BK is drawn in the triangle ABC. Determine the length of the BC side

The bisector ВK is drawn in the triangle ABC. Determine the length of the BC side if it is known that AK = 5, СK = 3, and the perimeter of the ABC triangle is 20.

In mathematics, there is a bisector theorem, according to which, it divides the opposite side in relation to the two adjacent sides of the triangle.

Base of triangle, side AC = 5 + 3 = 8

Suppose that side BC = x, therefore, times P of the triangle = 20, side AB = 20 – 8 – x = 12 – x

We compose an equation in which we use the ratio, according to the bisector theorem: x / (12 – x) = 3/5

5x = 36 – 3x

8x = 36

x = 4.5

Consequently: side BC = 4.5, and side AC = 12 – 4.5 = 7.5

Checking Along the Perimeter: P = 7.5 + 4.5 +8 = 20