In an isosceles triangle ABC, the sides AB and BC are 5 cm, the angle ABC is 36 degrees. The bisector CD

In an isosceles triangle ABC, the sides AB and BC are 5 cm, the angle ABC is 36 degrees. The bisector CD of a triangle is 3 cm. Find the ratio of the area of triangle DBC to the area of triangle ABC.

Let’s define the area of the triangle ABC.

Saavs = AB * BC * Sin360 = 5 * 5 * Sin36 = 25 * Sin36.

Since the triangle ABC is isosceles, the angle BAC = BCA = (180 – ABC) / 2 = (180 – 36) / 2 = 72.

СD is the bisector of the angle AСВ, then the angle AСD = ВСD = BCA / 2 = 72/2 = 36.

Then the AСD triangle is isosceles, ВD = СD = 3 cm.

Determine the area of the ВСD triangle.

Svsd = ВD * ВС * Sin36 = 3 * 5 * Sin36 = 15 * Sin36.

Then Sdvs / Savs = 25 * Sin36 / 15 * Sin36 = 5/3.

Answer: The area ratio of the triangles is 5/3.