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If the angles of a triangle are in the ratio 4 : 1 : 1, then the ratio of the longest side to the perimeter is
- a)√3 : (2 + 3)
- b)1 : 6
- c)1 : 2 + √3
- d)2 : 3
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the angles of a triangle are in the ratio 4 : 1 : 1, then the ratio...
Let the angles of the triangle be 4x, x, and x degrees, where x is a positive number.
The sum of the angles in a triangle is 180 degrees, so we have 4x + x + x = 180.
Simplifying the equation, we have 6x = 180.
Dividing both sides by 6, we have x = 30.
Therefore, the angles of the triangle are 120 degrees, 30 degrees, and 30 degrees.
Let the longest side be a, and the other two sides be b and c.
Using the Law of Sines, we have a/sin(120) = b/sin(30) = c/sin(30).
Simplifying, we have a/sqrt(3) = b/0.5 = c/0.5.
Therefore, a = sqrt(3)b and a = sqrt(3)c.
Adding these equations, we have a + a = sqrt(3)b + sqrt(3)c.
Simplifying, we have 2a = sqrt(3)(b + c).
The perimeter of the triangle is a + b + c.
Substituting the values, we have 2a = sqrt(3)(2a).
Dividing both sides by 2a, we have 1 = sqrt(3).
Therefore, the ratio of the longest side to the perimeter is 1:sqrt(3).
The sum of the angles in a triangle is 180 degrees, so we have 4x + x + x = 180.
Simplifying the equation, we have 6x = 180.
Dividing both sides by 6, we have x = 30.
Therefore, the angles of the triangle are 120 degrees, 30 degrees, and 30 degrees.
Let the longest side be a, and the other two sides be b and c.
Using the Law of Sines, we have a/sin(120) = b/sin(30) = c/sin(30).
Simplifying, we have a/sqrt(3) = b/0.5 = c/0.5.
Therefore, a = sqrt(3)b and a = sqrt(3)c.
Adding these equations, we have a + a = sqrt(3)b + sqrt(3)c.
Simplifying, we have 2a = sqrt(3)(b + c).
The perimeter of the triangle is a + b + c.
Substituting the values, we have 2a = sqrt(3)(2a).
Dividing both sides by 2a, we have 1 = sqrt(3).
Therefore, the ratio of the longest side to the perimeter is 1:sqrt(3).
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Community Answer
If the angles of a triangle are in the ratio 4 : 1 : 1, then the ratio...
The angles of a triangle are in the ratio of 4:1:1, then the ratio of largest side to perimeter is:
The angles of the triangle are 120 : 30 : 30,. since , 4x + ,x + x = 180 or, 6x=180 or ,. x = 30 so, 120, 30 and 30)
We Know
a/ SinA = b/ SinB = c/ SinC = K
a = K SinA = K Sin120 = √ 3/2
b = K SinB = K Sin30 = 1/2
c = K SinC = K Sin30 = 1/2
the ratio of largest side to perimeter is √ 3/2 / (√ 3/2 + 1)
= √ 3/ (√ 3 + 2) = √3: (√3+2)
The angles of the triangle are 120 : 30 : 30,. since , 4x + ,x + x = 180 or, 6x=180 or ,. x = 30 so, 120, 30 and 30)
We Know
a/ SinA = b/ SinB = c/ SinC = K
a = K SinA = K Sin120 = √ 3/2
b = K SinB = K Sin30 = 1/2
c = K SinC = K Sin30 = 1/2
the ratio of largest side to perimeter is √ 3/2 / (√ 3/2 + 1)
= √ 3/ (√ 3 + 2) = √3: (√3+2)
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If the angles of a triangle are in the ratio 4 : 1 : 1, then the ratio of the longest side to the perimeter isa)√3 : (2 + 3)b)1 : 6c)1 : 2 + √3d)2 : 3Correct answer is option 'A'. Can you explain this answer?
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If the angles of a triangle are in the ratio 4 : 1 : 1, then the ratio of the longest side to the perimeter isa)√3 : (2 + 3)b)1 : 6c)1 : 2 + √3d)2 : 3Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the angles of a triangle are in the ratio 4 : 1 : 1, then the ratio of the longest side to the perimeter isa)√3 : (2 + 3)b)1 : 6c)1 : 2 + √3d)2 : 3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the angles of a triangle are in the ratio 4 : 1 : 1, then the ratio of the longest side to the perimeter isa)√3 : (2 + 3)b)1 : 6c)1 : 2 + √3d)2 : 3Correct answer is option 'A'. Can you explain this answer?.
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