Question
Download Solution PDF∆ABC இல், AD என்பது மையக்கோடு மற்றும் G என்பது AD இல் உள்ள மையப்புள்ளியாகும், அதாவது AG : GD = 2 : 1. எனில் ar (∆BDG) : ar (∆ABC) எதற்குச் சமம்?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFநாம் அறிந்தபடி,
AD என்பது மையக்கோடு , எனவே AD முக்கோணத்தை இரண்டு சம பாகங்களாகப் பிரிக்கிறது
ar ΔADB = ar ΔADC
ΔABD இல்
⇒ ar ΔBDG/ar ΔBGA = DG/AG
⇒ ar ΔBDG/ar ΔBGA = 1/2
ΔBDG இன் பரப்பளவு= 1 அலகு என வைத்துக்கொள்ஓம்
எனவே, ΔBGA இன் பரப்பளவு = 2 அலகு
எனவே, ΔBAD இன் பரப்பளவு = ar ΔBDG + ar ΔBGA = 1 + 2 = 3 அலகு.
ΔABC இன் பரப்பளவு= 2 × ar ΔBAD = 2 × 3 = 6 அலகு.
∴ ar ΔBDG : ar ΔABC = 1 : 6.
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