wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Question 2
In a triangle ABC, E is the mid-point of the median AD.
Show that ar(ΔBED)=14ar(ΔABC)

Open in App
Solution

ED is the median of ΔEBC.
area(ΔBED)=area(ΔECD).....(1)
BE is the median of ΔABD.
area(ΔBED)=area(BEA).(2)
CE is the median for ΔADC.
area(ΔECD)=area(ΔEAC)(3)
i,e area(ΔBED)=area(ΔEAC) [ From (1)]……(4)
Now, area (ΔABC)=area(BEA)+area(ΔBED)+area(ΔECD)+area(ΔEAC)
area(ΔABC)=area(ΔBED)+area(ΔBED)+area(ΔBED)+area(ΔBED)[from(1),(2),(3) and (4)]
area(ABC)=4×area(ΔBED)
area(ΔBED)=14ar(ΔABC)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon