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(B)8.4cm(C) 4.2 cm(D) 0.525 cm4.In the adjoining figure, ABC and DBC are two triangles on the same base BC, AL i BC and DM.L BCarea (AABC)n, area (ADBc) is equal toAO2AO(A) OD(B) ODo ML.OD(C)(D) AOTAD |
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Answer» Construction:Draw AL ⟂ BC and DM ⟂BC . In ∆ ALO and ∆ DOM∠ALO = ∠DMO [each 90°]∠AOL = ∠DOM (vertically opposite angles)∆ALO ~ ∆ DMO (By AA Similarity criteria)AL/DM = AO/DO……………….(1) [corresponding sides of similar triangles are proportional]ar(∆ABC) =1/2 × BC × AL.. .. ... ...(2)ar(∆DBC) = 1/2×BC×DM………….(3)On dividing eq 2 and 3,ar(∆ABC)/ar(∆DBC) = 1/2×BC× AL/ ½ × BC ×DM ar(ABC) / ar (DBC) = AL/DMar(ABC) / ar (DBC) = AO/DO [from eq 1 ] |
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