Math Problem Statement

AD parçasi ABC üçbucağının tən bölənidir. AD=18 sm, AC=15 sm və BD-DC=2 sm olarsa, BD-ni tapın.

Solution

This question involves a triangle ABC with segment AD that divides the triangle. We are given that:

  • AD=18AD = 18 cm,
  • AC=15AC = 15 cm,
  • BDDC=2BD - DC = 2 cm.

The task is to find the length of BDBD.

Steps to approach the problem:

  1. The segment ADAD divides triangle ABCABC, and the difference between BDBD and DCDC is known.
  2. From the given information, we need to use the properties of triangle angle bisectors or proportionality relations.
  3. The proportionality rule states that if a segment in a triangle bisects an angle, it divides the opposite side into segments that are proportional to the adjacent sides.

We can set up a system using the information that BDDC=2BD - DC = 2 cm, and using the properties of angle bisectors to find BDBD.

Let me calculate this for you.From the problem setup, we know that ADAD is an angle bisector of triangle ABCABC, which implies that:

BDDC=ABAC\frac{BD}{DC} = \frac{AB}{AC}

We also know that BDDC=2BD - DC = 2 cm, and we are given AC=15AC = 15 cm. Let's define BD=xBD = x and DC=yDC = y. Therefore, the relationship between BDBD and DCDC becomes:

xy=2x - y = 2

Additionally, the proportionality equation from the angle bisector theorem is:

xy=ABAC\frac{x}{y} = \frac{AB}{AC}

Next, we can express ABAB in terms of ACAC and solve for BDBD and DCDC. However, without additional information about the sides of the triangle (such as the length of ABAB), the exact length of BDBD cannot be directly determined from the given data alone.

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Math Problem Analysis

Mathematical Concepts

Proportionality
Angle Bisector Theorem
Algebra

Formulas

BD - DC = 2
BD/DC = AB/AC (Angle Bisector Theorem)

Theorems

Angle Bisector Theorem

Suitable Grade Level

Grades 8-10