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
divide a line segment of length 14 cm internally in the ratio $2 : 5$. Also, justify your construction.
Given:
A line segment of length 14 cm.
To do:
We have to divide a line segment of length 14 cm internally in the ratio $2 : 5$.
Solution:
Steps of construction:
(i) Draw a line segment $AB = 14\ cm$.
(ii) Draw a ray $AX$ making an acute angle with $AB$.
(iii) From $B$, draw another ray $BY$ parallel to $AX$.
(iv) Cut off two equal parts from $AX$ and five parts from $BY$.
(v) Join $A_2$ and $B_5$ which intersects $AB$ at $P$.
$P$ is the required point which divides $AB$ in the ratio of $2 : 5$ internally.
Justification: In $\triangle \mathrm{AA}_{2} \mathrm{P}$ and $\triangle \mathrm{BB}_{5} \mathrm{P}$,
$\angle A_{2} A P=\angle P B B_{5}$ ($\angle A B Y=\angle B A X$)
$\angle \mathrm{APA}_{2}=\angle \mathrm{BPB}_{5}$ (Vertically opposite angles)
Therefore, by AA similarity,
$\triangle \mathrm{AA}_{2} \mathrm{P} \sim \Delta \mathrm{BB}_{5} \mathrm{P}$
This implies,
$\frac{A A_{2}}{B B_{5}}=\frac{A P}{B P}$
$\frac{A P}{B P}=\frac{2}{5}$
43 Views
