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If ABC be an equilateral triangle and AD perpendicular to BC Then
AB2 + BC2 + CA2 = ?
- a)3AD2
- b)5AD2
- c)2AD2
- d)4AD2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If ABC be an equilateral triangle and AD perpendicular to BC ThenAB2 ...
Let, the side of equilateral triangle is = a
Then AB = BC = CA = a
BD = DC = a/2
AB2 = AD2 + BD2
AC2 = AD2 + CD2
Add. Eq. (i) & (ii)
AB2 + AC2 = 2AD2 + BD2 + CD2
Add BC2 both sides
AB2 + AC2 + BC2
= 2AD2 + BD2 + CD2 + BC2
Put the value of side in R.H.S.
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Community Answer
If ABC be an equilateral triangle and AD perpendicular to BC ThenAB2 ...
Explanation:
Given:
- ABC is an equilateral triangle
- AD is perpendicular to BC
To Find:
We need to find the value of AB^2 + BC^2 + CA^2
Explanation:
- Since ABC is an equilateral triangle, all sides are equal. Let's assume the length of each side is 'a'.
- In an equilateral triangle, the altitude AD divides the triangle into two 30-60-90 right triangles.
- Therefore, BD = CD = a/2 and AD = a√3/2.
Calculations:
- AB^2 = AD^2 + BD^2 (Using Pythagoras theorem)
= (a√3/2)^2 + (a/2)^2
= 3a^2/4 + a^2/4
= a^2
- Similarly, BC^2 = CD^2 + BD^2
= (a/2)^2 + (a/2)^2
= a^2/4 + a^2/4
= a^2
- CA^2 = AD^2 + CD^2
= (a√3/2)^2 + (a/2)^2
= 3a^2/4 + a^2/4
= a^2
- Adding AB^2, BC^2, and CA^2:
AB^2 + BC^2 + CA^2 = a^2 + a^2 + a^2
= 3a^2
Therefore, AB^2 + BC^2 + CA^2 = 3AD^2
Conclusion:
Therefore, the correct option is d) 4AD^2.
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If ABC be an equilateral triangle and AD perpendicular to BC ThenAB2 + BC2 + CA2 = ?a)3AD2b)5AD2c)2AD2d)4AD2Correct answer is option 'D'. Can you explain this answer?
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