In a right angle triangle △ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of △ABD and △BCD?
Consider △ABD and △BCD:
∠BAD=∠DBC [Since, in △BDC, ∠DBC=90∘−∠C=∠A and in △ABC, ∠A=90∘−∠C]
By AA similarity criterion, △ADB∼△BDC
Option B is the odd one out among these options as can be seen from the above equation.