Q1 of 23 Page 192

ABC is a triangle. D is a point on AB such that and E is a point on AC such that If DE = 2 cm find BC.


Given:- DE=2cm




Formula used:- Line joining midpoints of 2 sides of triangle will be


half of its 3rd side.


Solution:-


Assume mid points of line AB and AC is M and N


The formation of new triangle will be there Δ AMN


As;


⇒ AC=4AE


and


∴ AM=2AE


Hence;


E is the midpoint of AM


Similarly


D is the midpoint of AN


→ In Δ AMN


If E,D are midpoints


ED=MN


MN=2ED


MN=2×2cm=4cm


→ In Δ ABC


If M,N are midpoints


AB=MN


AB=2MN


AB=2×4cm=8cm


Conclusion:-


BC=8cm


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