Question

ΔABC is an equilateral triangle such that AD ⊥ BC, then AD² =

(a)\(\frac32\) DC²

(b) 2 DC² 

(c) 3 CD² 

(d) 4 DC²

Answer 1

(c) 3CD²

In equilateral ΔABC, AD⊥BC

⇒ AD bisects the base BC 

⇒ BD = DC = \(\frac12BC=\frac12AB=\frac12AC\) 

Now use Pythagoras’ theorem in ΔADB.