Chapter: Similarity· Mathematics Part 2 (Geometry)
Answer: (i) 2 : 3 (ii) 2 : 5
\(\Delta ABD\), \(\Delta ADC\) and \(\Delta ABC\) all have the same height, the perpendicular from A to BC. So their areas are proportional to their bases.
(i) \(\dfrac{A(\Delta ABD)}{A(\Delta ADC)} = \dfrac{BD}{DC} = \dfrac{2}{3}\).
(ii) Let BD = 2k, DC = 3k, so BC = 5k. \(\dfrac{A(\Delta ABD)}{A(\Delta ABC)} = \dfrac{BD}{BC} = \dfrac{2k}{5k} = \dfrac{2}{5}\).