Question Number 224056 by fantastic last updated on 17/Aug/25
$${ABC}\:{is}\:{a}\:{triangle} \\ $$$${D}\:{is}\:{a}\:{point}\:{on}\:{AC}\:{such}\:{that} \\ $$$${AD}:{DC}=\mathrm{3}:\mathrm{2} \\ $$$${If}\bigtriangleup{ABC}=\mathrm{40}{u}^{\mathrm{2}} \\ $$$$\bigtriangleup{BDC}=?? \\ $$$${please}\:{help} \\ $$
Commented by fantastic last updated on 17/Aug/25
$${trig}.\:{not}\:{allowed} \\ $$
Answered by som(math1967) last updated on 17/Aug/25
$${ar}\bigtriangleup{ADC}:{ar}\bigtriangleup{BDC}={AD}:{DC}=\mathrm{3}:\mathrm{2} \\ $$$$\therefore\bigtriangleup{BDC}:\bigtriangleup{ABC}=\mathrm{2}:\mathrm{5} \\ $$$$\therefore\:\bigtriangleup{BDC}=\frac{\mathrm{2}}{\mathrm{5}}×\mathrm{40}=\mathrm{16}{u}^{\mathrm{2}} \\ $$