In \(\triangle ABC\), B–D–C and BD = 7, BC = 20 then find following ratios.
(1) \(\dfrac{A(\triangle ABD)}{A(\triangle ADC)}\) (2) \(\dfrac{A(\triangle ABD)}{A(\triangle ABC)}\) (3) \(\dfrac{A(\triangle ADC)}{A(\triangle ABC)}\)
Answer: (1) \(\frac{7}{13}\) (2) \(\frac{7}{20}\) (3) \(\frac{13}{20}\)
DC = BC − BD = 20 − 7 = 13.
Triangles ABD, ADC and ABC have the common vertex A and their bases BD, DC, BC lie on the same line, so they have the same height. Areas of triangles with equal heights are proportional to their bases.
\[\frac{A(\triangle ABD)}{A(\triangle ADC)} = \frac{BD}{DC} = \frac{7}{13}\] \[\frac{A(\triangle ABD)}{A(\triangle ABC)} = \frac{BD}{BC} = \frac{7}{20}\] \[\frac{A(\triangle ADC)}{A(\triangle ABC)} = \frac{DC}{BC} = \frac{13}{20}\]Log in or create a free account to answer this question.
