Question

ABC is a equilateral triangle of side 2a.find each of its altitude​

Answer 1

the triangle of two side is equal then triangle is equal

Answer 2

Given: ∆ABC is an equilateral triangle with side 2a.

Construction: Draw altitude AD such that AD is perpendicular to BC.

To find: AD

Solution: In ∆ADB and ∆ADC,

AB = AC (Both sides are 2a)

AD = AD (Common side)

<ADB=<ADC (Both 90° as AD

perpendicular to BC)

Hence, ∆ADB ~ ∆ADC (By R.H.S congurancy)

Hence, BD = DC ( By cpct )

BD = DC

BD = DC = 1/2 BC

BD = DC = 2a/2

BD = DC = a

Hence, BD = a

In right ∆ADB,

by using Pythagoras theorem,

(AB)^ = (AD)^ + (BD)^

(2a)^ = (AD)^ + (a)^

4a^ = (AD)^ + a^

4a^ - a^ = (AD)^

3a^ = (AD)^

AD = √3a^

AD = a√3

Thus, the length of altitude AD = a√3

Similarly, CF = BE = a√3