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the Fig 4.128, LM I NQ and LNEPO IE MP-MNFind ar (ALMN) : ar (AQNP)Fig. 412s |
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Answer» Sol:Given LM || NQ ⇒ ∠1 = ∠4 [Alternate interior angles cut by transversal MN] Again, LN || PQ⇒ ∠2 = ∠3 [Alternate interior angles cut by transversal MN]∴ ΔLMN ~ ΔNPQ [AA criterion of similarity]Area of ΔLMN / Area of ΔNPQ = MN2/ NP2But MP = 1/3 MN⇒ NP = 2/3 MNArea of ΔLMN / Area of ΔNPQ = MN2/ NP2= MN2/ (2/3 MN)2= (3/2)2= 9/4. |
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