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If PA is the median of the equilateral triangle PQR and G be the centroid, then what is the ratio of (PG + GA) ∶ (PG - GA)?
- a)4 ∶ 1
- b)3 ∶ 1
- c)2 ∶ 1
- d)3 ∶ 2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If PA is the median of the equilateral triangle PQR and G be the centr...
Since given triangle is equilateral
So, the ratio of centroid on median 2 : 1 or PG : GA = 2 : 1
(PG + GA) : (PG - GA) = 2 + 1/2 - 1 = 3 : 1
So, the ratio of centroid on median 2 : 1 or PG : GA = 2 : 1
(PG + GA) : (PG - GA) = 2 + 1/2 - 1 = 3 : 1
Most Upvoted Answer
If PA is the median of the equilateral triangle PQR and G be the centr...
Given Information:
PA is the median of the equilateral triangle PQR and G is the centroid of the triangle.
Concept of Centroid in an Equilateral Triangle:
- In an equilateral triangle, the centroid divides the median in the ratio 2:1.
- This means that PG:GA = 2:1.
Finding the Ratio of (PG + GA)(PG - GA):
- Let's assume PG = 2x and GA = x (based on the ratio 2:1).
- (PG + GA) = 2x + x = 3x
- (PG - GA) = 2x - x = x
- Therefore, the required ratio is (3x)(x) = 3x^2
Calculating the Ratio:
- We have found that the ratio is 3x^2.
- Since PG:GA = 2:1, we can substitute x = 1.
- Therefore, the ratio becomes 3(1)^2 = 3.
Final Answer:
- The ratio of (PG + GA)(PG - GA) is 3.
- Hence, the correct answer is option 'B' (3).
PA is the median of the equilateral triangle PQR and G is the centroid of the triangle.
Concept of Centroid in an Equilateral Triangle:
- In an equilateral triangle, the centroid divides the median in the ratio 2:1.
- This means that PG:GA = 2:1.
Finding the Ratio of (PG + GA)(PG - GA):
- Let's assume PG = 2x and GA = x (based on the ratio 2:1).
- (PG + GA) = 2x + x = 3x
- (PG - GA) = 2x - x = x
- Therefore, the required ratio is (3x)(x) = 3x^2
Calculating the Ratio:
- We have found that the ratio is 3x^2.
- Since PG:GA = 2:1, we can substitute x = 1.
- Therefore, the ratio becomes 3(1)^2 = 3.
Final Answer:
- The ratio of (PG + GA)(PG - GA) is 3.
- Hence, the correct answer is option 'B' (3).
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Community Answer
If PA is the median of the equilateral triangle PQR and G be the centr...
Since given triangle is equilateral
So, the ratio of centroid on median 2 : 1 or PG : GA = 2 : 1
(PG + GA) : (PG - GA) = 2 + 1/2 - 1 = 3 : 1
So, the ratio of centroid on median 2 : 1 or PG : GA = 2 : 1
(PG + GA) : (PG - GA) = 2 + 1/2 - 1 = 3 : 1
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If PA is the median of the equilateral triangle PQR and G be the centroid, then what is the ratio of (PG + GA)(PG - GA)?a)41b)31c)21d)32Correct answer is option 'B'. Can you explain this answer?
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If PA is the median of the equilateral triangle PQR and G be the centroid, then what is the ratio of (PG + GA)(PG - GA)?a)41b)31c)21d)32Correct answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If PA is the median of the equilateral triangle PQR and G be the centroid, then what is the ratio of (PG + GA)(PG - GA)?a)41b)31c)21d)32Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If PA is the median of the equilateral triangle PQR and G be the centroid, then what is the ratio of (PG + GA)(PG - GA)?a)41b)31c)21d)32Correct answer is option 'B'. Can you explain this answer?.
If PA is the median of the equilateral triangle PQR and G be the centroid, then what is the ratio of (PG + GA)(PG - GA)?a)41b)31c)21d)32Correct answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If PA is the median of the equilateral triangle PQR and G be the centroid, then what is the ratio of (PG + GA)(PG - GA)?a)41b)31c)21d)32Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If PA is the median of the equilateral triangle PQR and G be the centroid, then what is the ratio of (PG + GA)(PG - GA)?a)41b)31c)21d)32Correct answer is option 'B'. Can you explain this answer?.
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