- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
In $ \triangle \mathrm{XYZ} $, the bisector of $ \angle X $ intersects $ Y Z $ at $ M $. If $ X Y=8, X Z=6 $ and $ M Z=4.8 $, find YZ.
Given:
In \( \triangle \mathrm{XYZ} \), the bisector of \( \angle X \) intersects \( Y Z \) at \( M \).
\( X Y=8, X Z=6 \) and \( M Z=4.8 \).
To do:
We have to find \( YZ \).
Solution:
We know that,
An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
Therefore,
$\frac{XY}{XZ}=\frac{YM}{MZ}$
$\frac{8}{6}=\frac{YM}{4.8}$
$YM=\frac{4.8\times4}{3}$
$YM=6.4$
$\Rightarrow YZ=YM+MZ=6.4+4.8=11.2\ cm$
Hence, the value of $YZ$ is $11.2\ cm$.
Advertisements