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Question
In Δ ABC , MN || BC .
If BC = 14 cm and MN = 6 cm , find `("Ar" triangle "AMN")/("Ar" . ("trapezium MBCN"))`
Solution
Δ AMN - Δ ABC {proved above in (a)}
`("Ar" triangle "AMN")/("Ar" triangle "ABC") = ("MN"/"BC")^2 = (6/14)^2 = 9/49`
`("Ar" triangle "AMN")/(("Ar" triangle "AMN") + "Ar" . ("trapezium MBCN")) = 9 / 49`
49 Ar. Δ AMN = 9 Ar. Δ AMN + 9 Ar .(trapezium MBCN)
40 Ar. Δ AMN = 9 Ar.( trapezium MBCN)
`("Ar" triangle "AMN")/("Ar" . ("trapezium MBCN")) = 9/40`
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