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Let a, b, c be the lengths of the sides of a triangle ABC, while p, q, r be the lengths of the sides of another triangle PQR. If p2/a = q2/b = r2/c = Perimeter of Triangle ABC, then what can be inferred about the nature of the triangle PQR?
  • a)
    Acute angled Triangle
  • b)
    Right angled triangle
  • c)
    Obtuse angle Triangle
  • d)
    None of These
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Let a, b, c be the lengths of the sides of a triangle ABC, while p, q...
P2/a = q2/b = r2/c = P, where P is the perimeter of Triangle ABC
Thus p2 + q2 = (a + b)P
Similarly r2 = cP
But we know that for any Triangle, sum of any two sides is greater than 3rd side, (a +b) > c
Thus we get p2 + q2 > r2
Similarly p2 + r2 > q2 and r2 + q2 > p2
Hence Triangle PQR is an acute angled Triangle.
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Let a, b, c be the lengths of the sides of a triangle ABC, while p, q, r be the lengths of the sides of another triangle PQR. If p2/a = q2/b = r2/c = Perimeter of Triangle ABC, then what can be inferred about the nature of the triangle PQR?a)Acute angled Triangleb)Right angled trianglec)Obtuse angle Triangled)None of TheseCorrect answer is option 'A'. Can you explain this answer?
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