In ABC, B – D – C and BD = 7, BC = 20 then find following ratios.

Given BD = 7, BC = 20
Construction:
Draw a perpendicular from A to BC meeting at E.
BC = BD+DC
20 = 7+DC
DC = 13
(1)A( ABD) /A( ADC) = BD/DC [Triangles having same height]
A( ABD) /A( ADC) = 7/13
(2) A( ABD) /A( ABC) = BD/BC [Triangles having same height]
A( ABD) /A( ABC) = 7/20
(3) A( ADC) /A( ABC) = DC/BC [Triangles having same height]
A( ADC) /A( ABC) = 13/20