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Question
In Δ ABC , MN || BC .
If `"AB"/"AM" = 9/4` , find `("Ar" ("trapezium MBCN"))/("Ar" . (triangle "ABC"))`
Solution
Δ AMN ∼ ΔABC {proved above}
`("Ar" triangle "AMN")/("Ar" triangle "ABC") = "AM"^2/"AB"^2 = (4/9)^2 = 16/81`
`("Ar" triangle "ABC" - "Ar" ("trapezium MBCN"))/("Ar" . triangle "ABC") = 16/81`
81 × Ar. Δ ABC - 81 × Ar. (trapezium MBCN) = 16 × Ar. Δ ABC
64 Ar. Δ ABC = 81 Ar .(trapezium MBCN)
`("Ar" ("trapezium MBCN"))/("Ar".(triangle "ABC")) = 65/81`
i.e. 65 : 81
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