In a right angled △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:
Since, in △BDC, ∠DBC=90∘−∠C=∠A and in △ABC,∠A=90∘−∠C,
and ∠BDA=∠BDC [90∘]
By AA similarity criterion, △ADB∼△BDC
Thus, the option (ABAC)2 is required answer.