Question

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

Answer 1

Answer:

√3a

Step-by-step explanation:

altitude of equilateral triangle=(√3)*(side)/2

where side=2a

Answer 2

Given:

• ABC is an equilateral triangle with side 2a.

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To find:

• Length of each altitudes.

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Solution:

• As we can see the first figure.

In ∆ABD and ∆ACD

• AB = AC .... [Given]
• AD = AD .... [Common]
• ∠ADB = ∠ADC .... [Each 90°]

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•°• ∆ABD ≅ ∆ACD ..... [By RHS congruency]

★ BD = DC [CPCT]

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Then we can write that

→ BD + DC = BC

→ BD + BD = 2a

→ 2BD = 2a

→ BD = a

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As we can see that ∆ABD is a right angled triangle, so applying pythagoras theorem.

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→ AB² = BD² + AD²

→ (2a)² = (a)² + AD²

→ 4a² = a² + AD²

→ AD² = 4a² - a²

→ AD² = 3a²

→ AD = √3a²

→ AD = a√3

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Similarly,

[In figure 2]

• CF = a√3
• BE = a√3

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Hence,

• Length of each altitude is a√3 units.