Question

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

A.\(\frac{3}2\) DC² 

B. 2 DC² 

C. 3 CD² 

D. 4 DC²

Answer 1

Given in an equilateral ΔABC, AD ⊥ BC

Since AD ⊥ BC, BD = CD = BC/2 

We know that the Pythagoras theorem state that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

Now, in right triangle ADC, 

⇒ AC² = AD² + DC² 

⇒ BC² = AD² + DC² 

⇒ (2DC)² = AD² + DC² 

⇒ 4DC² = AD² + DC² 

⇒ 3DC² = AD² 

∴ 3CD² = AD²