Question
Download Solution PDF\(\Delta XYZ \sim \Delta GST\) మరియు XY ∶ GS = 2 ∶ 3, XV అనేది భుజం YZ యొక్క మధ్యగతం, మరియు GD అనేది భుజం ST యొక్క మధ్యగతం. \(({\frac{{YV}}{{SD}}}) ^2\) యొక్క విలువ _______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఇచ్చినది:
XY ∶ GS = 2 ∶ 3
ఉపయోగించిన భావన:
రెండు భుజాలు మరియు త్రిభుజం యొక్క మూడవ భాగాన్ని విభజించే మధ్యగతం వరుసగా సంబంధిత భుజాలకు మరియు మరొక త్రిభుజం మధ్యగతానికి అనులోమానుపాతంలో ఉంటే, అప్పుడు రెండు త్రిభుజాలు సమానంగా ఉంటాయి.
గణన:
\(\Delta XYZ \sim \Delta GST\)
కాబట్టి, \(({\frac{{YV}}{{SD}}}) ^2\) = \(({\frac{{XY}}{{GS}}}) ^2\)
⇒ \(({\frac{{2}}{{3}}}) ^2\)
⇒ \(\frac{4}{9}\)
∴ \(({\frac{{YV}}{{SD}}}) ^2\) విలువ \(\frac{4}{9}\).
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