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TS EAMCET · Maths · Properties of Triangles

If \(\mathrm{p}_1, \mathrm{p}_2, \mathrm{p}_3\) are the altitudes and \(a=4, b=5, c=6\) are the sides of a triangle ABC, then \(\frac{1}{\mathrm{p}_1{ }^2}+\frac{1}{\mathrm{p}_2{ }^2}+\frac{1}{\mathrm{p}_3{ }^2}=\)

  1. A \(\frac{77}{225}\)
  2. B \(\frac{44}{225}\)
  3. C \(\frac{308}{225}\)
  4. D \(\frac{22}{75}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{44}{225}\)

Step-by-step Solution

Detailed explanation

\(s = \frac{a+b+c}{2} = \frac{4+5+6}{2} = \frac{15}{2}\) \(A^2 = s(s-a)(s-b)(s-c) = \frac{15}{2}(\frac{15}{2}-4)(\frac{15}{2}-5)(\frac{15}{2}-6)\) \(A^2 = \frac{15}{2} \cdot \frac{7}{2} \cdot \frac{5}{2} \cdot \frac{3}{2} = \frac{1575}{16}\)…