A REVISIT In ALMN, a line AB is such that AB || MN and AB line bisect the area of a triangle in two equal parts. Then, find LA: MA?
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Correct option is
D
15:1
In △LPQ and △LMN
∠L ≅∠L [Common angle]
∠LPQ ≅∠LMN [Corresponding angles]
∴ △LPQ ≅ △LMN [By AA test of similarity]
ar(LMN)ar(LPQ) = LM2LP2 [Areas of similar triangles]
∴ar(LMN)ar(LPQ) = 8222
∴ ar(LMN)ar(LPQ) = 644
∴ ar(LMN)ar(LPQ) = 161
∴ ar(LPQ)ar(LMN) = 116 [By Invertendo]
∴ar(LPQ)ar(LMN)−ar(LPQ)= 116−1
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