3. In Fig. 11.46, if angle CBD > angle BCE then prove that AB > AC
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Given: Coordinates of Point A(1,3),B(−1,0) and C(4,0)
Construction: Drop a perpendicular from A on x− axis, which meets x-axis at D≡(1,0)
Now in ΔADC,AD=3,DC=3
Area of ΔADC=21×DC×AD
=21×3×3=29 cm2
Now in ΔADB,AD=3,DB=2
Area of ΔADB=21×DB×AD
=21×2×3=3 cm2
Area of ΔABC= Ara of ΔADC+ Area of ΔABD
=29+3=215=7.5 cm2
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