We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
57
1
avatar

We have triangle $\triangle ABC$ where $AB = AC$ and $AD$ is an altitude. Meanwhile, $E$ is a point on $AC$ such that $AB \parallel DE.$ If $BC = 12$ and the area of $\triangle ABC$ is $180,$ what is the area of $ABDE$?

 Jul 15, 2019
 #1
avatar+102386 
+1

See the following image......

 

Let  A = (6,30)   B = (0, 0)   C = ( 12,0)   D  = (6,0)    and AD  = 30

 

Since ED is parallel to AB.....then ang;e EDC  = angle ABC

And angle ACB  = angle ECD

So triangle ABC will be similar to triangle EDC

And  the base of EDC  = DC is 1/2 of base BC....so

 

The area of triangle EDC  = Area of triangle ABC * (scale factor of EDC to ABC)^2  =

 

!80 * (1/2)^2  =   180 * (1/4)  = 45 units^2

 

So....[ ABDE]  = [ ABC ] - [EDC]  =  180 - 45   = 135 units^2

 

 

cool cool cool

 Jul 15, 2019

16 Online Users

avatar