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

BL and CM are medians of ΔABC right angled at A. Prove that 4(BL2+CM2)=5BC2.

Open in App
Solution

Given:ABCisrightangledatA.BLandCMareitsmediansToProve:Proof:InBALBL2=AL2+AB2...(1)[UsingPythagorastheorem]InCAMCM2=AM2+AC2.....(2)[UsingPythagorastheorem]Adding(1)and(2)andthenmultiplyingby4,weget4(BL2+CM2)=4(AL2+AB2+AM2+AC2)=4AL2+AM2+(AB2+AC2)=4AL2+AM2+BC2[InrightangleABCAB2+AC2=BC2]=4(AL2+AM2+BC2)=4(ML2+BC2)[InLAMAL2+AM2=ML2]=4ML2+4BC2[Accordingtomidpointtheormalinejoiningmidpointsoftwosidesisparalleltothirdsideandisequaltohalfofit,ML=BC2]=BC2+4BC2=5BC2.Henceproved.\quad

319048_327522_ans_d0bf5ed1453e4af28951b0a3d8923e0f.bmp

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Triangle
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon