[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 122: include(/home/shoeb/public_html/www.matholympiad.org.bd/forum/includes/phpbb-latex.php) [function.include]: failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 122: include() [function.include]: Failed opening '/home/shoeb/public_html/www.matholympiad.org.bd/forum/includes/phpbb-latex.php' for inclusion (include_path='.:/opt/php53/lib/php')
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 122: include(/home/shoeb/public_html/www.matholympiad.org.bd/forum/includes/phpbb-latex.php) [function.include]: failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 122: include() [function.include]: Failed opening '/home/shoeb/public_html/www.matholympiad.org.bd/forum/includes/phpbb-latex.php' for inclusion (include_path='.:/opt/php53/lib/php')
[phpBB Debug] PHP Warning: in file [ROOT]/includes/session.php on line 1042: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3887)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4786: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3887)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4788: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3887)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4789: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3887)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4790: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3887)
BdMO Online Forum • View topic - BDMO 2016: National Junior/2

BDMO 2016: National Junior/2

For students of class 6-8 (age 12 to 14)
Facebook Twitter

BDMO 2016: National Junior/2

Post Number:#1  Unread postby Tasnova Novera » Mon Feb 06, 2017 6:56 pm

Please help me solving BDMO 2016: National Junior/ Question No. 2

The Question is:
ABC is a triangular piece of paper with an area of 500 square units and AB = 20 units. DE is parallel to AB. The triangle is folded along DE. The part of the triangle below AB has an area of 80 square units. What is the area of CDE?

Ref.
http://www.matholympiad.org.bd/question ... 6-national
Tasnova Novera
 
Posts: 1
Joined: Fri Feb 03, 2017 10:32 pm

Re: BDMO 2016: National Junior/2

Post Number:#2  Unread postby Zahin Hasin Rudro » Thu Aug 03, 2017 11:13 pm

[CDE]=225 sq. units
Zahin Hasin Rudro
 
Posts: 11
Joined: Sun Jul 12, 2015 3:52 am

Re: BDMO 2016: National Junior/2

Post Number:#3  Unread postby abrarfiaz » Thu Oct 12, 2017 11:41 am

explain the process please
abrarfiaz
 
Posts: 4
Joined: Mon Mar 20, 2017 4:53 pm

Re: BDMO 2016: National Junior/2

Post Number:#4  Unread postby abrarfiaz » Sat Nov 18, 2017 8:02 pm

can u explain please?
abrarfiaz
 
Posts: 4
Joined: Mon Mar 20, 2017 4:53 pm

Re: BDMO 2016: National Junior/2

Post Number:#5  Unread postby Tasnood » Fri Dec 01, 2017 2:07 pm

Capture.PNG
[Image may not be appropriate]
Capture.PNG (16.4 KiB) Viewed 50 times
Let $CF'G'$ be the reflection of $C'FG$. And as $CDE$ is the reflection of $C'DE$, we can say,
$F'G'||DE||AB$
So, $(CF'G')=(C'FG)=80$.
(ABC)=$\frac{1}{2}AB.CP=500$ or, $10CP=500$ or,$CP=50$
We know, $\triangle ABC~\triangle CF'G'$
$\frac {AB}{F'G'}=\frac {CP}{CQ}=k$
So, $F'G'=\frac{AB}{k}=\frac{20}{k}$, $CQ=\frac{CP}{k}=\frac{50}{k}$
$(CF'G')=\frac{CQ.F'G'}{2}=\frac{20*50}{2.k.k}=\frac{500}{k.k}=80$ or,$k=\frac{5}{2}$
$FG=F'G'=\frac{20}{k}=8$, $CQ=\frac{50}{k}=20$
Then, $CP+C'P'=50+20=70$ or,$CQ+C'P'+PR+RQ=70$ or,$2CR=70$ or,$CR=35$
We proved, $\triangle CF'G'~\triangle CDE$
So, $\frac{DE}{F'G'}=\frac{CR}{CQ}=\frac{35}{20}=\frac{7}{4}$
$DE=\frac{7F'G'}{4}=\frac{7*8}{4}=14$
So, $(CDE)=\frac{1}{2}DE.CR=\frac{14*35}{2}=245$; that we need. :P
User avatar
Tasnood
 
Posts: 11
Joined: Tue Jan 06, 2015 1:46 pm


Share with your friends: Facebook Twitter

  • Similar topics
    Replies
    Views
    Author

Return to Junior Level

Who is online

Users browsing this forum: No registered users and 2 guests