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AP EAMCET · Maths · Properties of Triangles

In a triangle \(\mathrm{ABC}\) if \(2 r_1=3 r_2=r_3\) then \(\mathrm{a}: \mathrm{b}: \mathrm{c}=\)

  1. A \(4: 3: 5\)
  2. B \(3: 4: 5\)
  3. C \(5: 3: 4\)
  4. D \(3: 5: 4\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(4: 3: 5\)

Step-by-step Solution

Detailed explanation

\(2 r_1 = 3 r_2 \implies \frac{2}{s-a} = \frac{3}{s-b} \implies 2(s-b) = 3(s-a) \implies 2s - 2b = 3s - 3a \implies s = 3a - 2b\) \(3 r_2 = r_3 \implies \frac{3}{s-b} = \frac{1}{s-c} \implies 3(s-c) = s-b \implies 3s - 3c = s - b \implies 2s = 3c - b\)…