- Trending Categories
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 figure, BELT is a rhombus. Diagonals ET and BL meet at the point O. If OT = (x), OL = (x $-$ 1) and TL = (x $+$ 1). Find the length of TL.
Given: BELT is a rhombus. Diagonals ET and BL meet at the point O. If OT = (x), OL = (x $-$ 1) and TL = (x $+$ 1).
To find: Here we have to find the length of TL.
Solution:
As we know diagonal of a rhombus are perpendicular and bisect each other.
Therefore Using Pythagoras Theorem:
$P^{2} \ +\ B^{2} \ =\ H^{2}$
$( OL)^{2} \ +\ ( OT)^{2} \ =\ ( TL)^{2}$
$( x\ -\ 1)^{2} \ +\ ( x)^{2} \ =\ ( x\ +\ 1)^{2}$
$x^{2} \ +\ 1\ -\ 2x\ +\ x^{2} \ =\ x^{2} \ +\ 1\ +\ 2x$
$2x^{2} \ +\ 1\ -\ 2x\ -\ x^{2} \ -\ 1\ -\ 2x\ =\ 0$
$x^{2} \ -\ 4x\ =\ 0$
$x( x\ -\ 4) \ =\ 0$
So,
$x\ =\ 0\ or\ x\ =\ 4$
As value of $x$ can't be equal to 0, so, $x$ is equal to 4.
Now,
TL = $x\ +\ 1$
TL = 4 $+$ 1
TL = 5 unit
So, the answer is 5 unit.
32 Views
