Question

if ABC is an equilateral triangle such that AD perpendicular to BC , then AD^w2 is equal to DC respect to what value

Answer 1

Heya User,

Let AB = a;
We know height of an Equilateral Δ is [ √3 / 2 ] * side :->
=> AD = [ √3 / 2 ] a 

Also, perpendicular to the base in an equiangular triangle bisects the base:--> Hence DC = [ 1/2 ] a

Now, Acc. to ur Question -> 
----> Let's Assume :-> AD² = xDC
=> [ 3/4 ] a² = 1/2ax
=> [ 3/2 ] a² = ax
=> 3a² = 2ax
=> 3a = 2x
=> x = 3/2 a 

Now, 1/2 a = DC => x = 3/2 a = 3* [ 1/2 a ] = 3DC

Sooo, AD² = xDC = 3DC [ DC ] = 3DC²

.'. AD² = 3DC²