Question

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

Answer 1

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refer the attachment :)

Answer 2

Given:-

• ∆ABC is an equilateral triangle with each side "2a".
• Altitude AD is perpendicular on BC.

To Find:-

• AD

Solution:-

→ AB = BC = AC = 2a

→ AD = AD ( Common )

→ ∠ADB = ∠ADC ( Each of 90° )

★By SAS congruency rule,

→ ∆ADB ≅ ∆ ADC

•°• BD = a, DC = a

★In right ∆ ADB

→ AB^2 = AD^2 + BD^2

→ (2a)^2 = AD^2 + a^2

→ 4a^2 = AD^2 + a^2

→ AD^2 = 4a^2 - a^2

→ AD ^2 = 3a^2

→ AD = (√3a)^2

→ AD = √3a

Hence,

• AD = √3a