In an isosceles triangle ABC, the segment BD is the bisector drawn to the base.

In an isosceles triangle ABC, the segment BD is the bisector drawn to the base. Find its length if the perimeter of triangle ABC is 28 cm and the perimeter of triangle ABD is 20 cm.

In an isosceles triangle, the bisector is. drawn to the base is the median, which means that blood pressure = CD.

Let us introduce the notation. Let AB = BC = x, and AD = CD = y.

Let us express the perimeter of the triangle ABC: P (ABC) = AB + BC + AC = 28 cm.

x + x + 2y = 28.

2x + 2y = 28;

2 (x + y) = 28;

x + y = 14.

Let us express the perimeter of the triangle ABD: P (ABD) = AB + BD + AD = 20 cm.

x + BD + y = 20.

(x + y) + BD = 20.

Since x + y = 14, it turns out that 14 + BD = 20;

BD = 20 – 14 = 6 cm.

Answer: the length of the bisector BD = 6 cm.