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Diagonals LS and BN of rectangle BSNL intersect each other at point K. If KL =7cm, find LS and BN (see fig)
184373.jpg

Solution
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InparallelogramBSNL,BS=LN&BSLN.IfBSLN&BNisthetransversalthenLNK=SBK{Alternateangles}IfBSLN&SListhetransversalthenKLN=KSB{Alternateangles}InLKN&SKB,LNK=SBKBS=LNKLN=KSBSoLKNSKB{ByASARuleofCongruency}SoKL=SKGivenKL=7cmLS=2KL=2×7=14cmInarectanglebothdiagonalsareequal,soBN=LS=14cm

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