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Directions: Consider the following:
In a triangle ABC, a, b and c are the lengths of the sides and p, q and r are the lengths of its medians.
Q. Which one of the following is correct?
  • a)
    2(p + q + r) = (a + b + c)
  • b)
    2(p + q + r) > 3(a + b + c)
  • c)
    2(p + q + r) < 3(a + b + c)
  • d)
    11(p + q + r) > 10(a + b + c)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Directions:Consider the following:In a triangle ABC, a, b and c are th...

Sum of two sides of a triangle > third side
In triangle ABD,
AB + BD > AD       ---- 1
In triangle ACD
AC + CD > AD        ---- 2
Adding the inequalities 1 and 2
AB + BD + CD + AC > 2AD
AB + BC + AC > 2 AD
a + b + c > 2p
Similarly for other medians
a + b + c > 2q
a + b + c > 2r
Adding all the inequalities
3(a + b + c) > 2(p + q + r)
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Directions:Consider the following:In a triangle ABC, a, b and c are the lengths of the sides and p, q and r are the lengths of its medians.Q.Which one of the following is correct?a)2(p + q + r) = (a + b + c)b)2(p + q + r) > 3(a + b + c)c)2(p + q + r) < 3(a + b + c)d)11(p + q + r) > 10(a + b + c)Correct answer is option 'C'. Can you explain this answer?
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Directions:Consider the following:In a triangle ABC, a, b and c are the lengths of the sides and p, q and r are the lengths of its medians.Q.Which one of the following is correct?a)2(p + q + r) = (a + b + c)b)2(p + q + r) > 3(a + b + c)c)2(p + q + r) < 3(a + b + c)d)11(p + q + r) > 10(a + b + c)Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Directions:Consider the following:In a triangle ABC, a, b and c are the lengths of the sides and p, q and r are the lengths of its medians.Q.Which one of the following is correct?a)2(p + q + r) = (a + b + c)b)2(p + q + r) > 3(a + b + c)c)2(p + q + r) < 3(a + b + c)d)11(p + q + r) > 10(a + b + c)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions:Consider the following:In a triangle ABC, a, b and c are the lengths of the sides and p, q and r are the lengths of its medians.Q.Which one of the following is correct?a)2(p + q + r) = (a + b + c)b)2(p + q + r) > 3(a + b + c)c)2(p + q + r) < 3(a + b + c)d)11(p + q + r) > 10(a + b + c)Correct answer is option 'C'. Can you explain this answer?.
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