The largest angle of a triangle, whose sides are 12, 18 and 20 inches, is bisected. Find the
lengths of the segments created when the angle bisector intersects the opposite side of the
triangle.

The angle bisector theorem states that the angle bisector of a triangle will divide the a side, such that their lengths will be proportional the the other two sides of the triangle.

The triangle is shown in the diagram attached below. The angle bisected is opposite the side measuring 20 inches.

According to the angle bisector theorem, therefore:

AB/AC = x/y

Substitute

12/18 = BD/DC

2/3 = BD/DC

This implies that:

2x + 3x = 20

5x = 20

x = 4

Therefore:

BD = 2x

Plug in the value of x

BD = 2 × 4 = 8 inches

Dc = 3x = 3 × 4 = 12 inches.

Therefore, applying the angle bisector theorem, the lengths of the segments are: 8 inches and 12 inches.

Learn more about angle bisector theorem on:

https://brainly.com/question/2478436

The largest angle of a triangle, whose sides are 12, 18 and 20 inches, is bisected. Find the lengths of the segments created when the angle bisector intersects the opposite side of the triangle.

Respuesta :

What is the Angle Bisector Theorem?

Otras preguntas

The largest angle of a triangle, whose sides are 12, 18 and 20 inches, is bisected. Find the
lengths of the segments created when the angle bisector intersects the opposite side of the
triangle.