If ABC is an equilateral triangle of side a, prove that its altitude =√32a [3 MARKS]
Concept: 1 Mark
Application: 1 Mark
Proof : 1 Mark
ΔABC is an equilateral triangle.
We are given that AB = BC = CA = a. AD is the altitude, i.e., AD⊥BC.
Now, in right angled triangles ABD and ACD, we have
AB=AC [Given]
and AD=AD [Common side]
⇒ΔABD∼ΔACD [By RHS congruence]
⇒BD=CD [ C.P.C.T]
⇒BD=12BC=a2
From right triangle ABD,
AB2=AD2+BD2
⇒a2=AD2+(a2)2
⇒AD2=a2−a24=34a2
⇒AD=√3a2