Question

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

i. A(∆ABD)/A(∆ADC)

ii. A(∆ABD)/A(∆ABC)

iii. A(∆ADC)/A(∆ABC)

Answer 1

Draw AE ⊥ BC, B – E – C. BC = BD + DC [B – D – C]

∴ 20 = 7 + DC 

∴ DC = 20 – 7 = 13 

i. ∆ABD and ∆ADC have same height AE. 

A(ΔABD)/A(ΔADC) = BD/DC [Triangles having equal height]

∴ A(ΔABD)/A(ΔADC) = 7/13

ii. ∆ABD and ∆ABC have same height AE. 

A(∆ABD)/A(∆ABC) = 7/20 [Triangles having equal height] 

∴ A(ΔABD)/A(ΔABC) = 7/20 

iii. ∆ADC and ∆ABC have same height AE. 

A(ΔADC)/A(ΔABC) = DC/BC [Triangles having equal height]

∴ A(ΔADC)/A(ΔABC) = 13/20