Question

In ∆ABC, seg MN || side AC. seg MN divides ∆ABC into two parts equal in area. determine AM/MB

Answer 1

AM/MB  = 1/√2 In ∆ABC, seg MN || side AC. seg MN divides ∆ABC into two parts equal in area.

Step-by-step explanation:

In ∆ABC, seg MN || side AC

=> ΔAMN ≈  ∆ABC

=> AM/AB  =  AN/AC  = MN/BC

Area of ΔAMB/ Area of Δ ABC  =  (AM/MB)²

MN divides ∆ABC into two parts equal in area

=> Area of Δ ABC = 2 Area of ΔAMB

=> Area of ΔAMB/ 2 Area of ΔAMB  =  (AM/MB)²

=> 1/2 =  (AM/MB)²

=> AM/MB  = 1/√2

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