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AP EAMCET · Maths · Properties of Triangles

In a \(\triangle \mathrm{ABC}\) if \(a=13, b=14, c=15\) then \(r_1=\)

  1. A \(\frac{23}{2}\)
  2. B \(\frac{21}{2}\)
  3. C \(\frac{25}{2}\)
  4. D \(\frac{26}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{21}{2}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \quad a=13, b=14, c=15 \Rightarrow \mathrm{~s}=\frac{a+b+c}{2}=21 \\ & \text { Area }(\Delta)=\sqrt{\mathrm{s}(\mathrm{s}-13)(\mathrm{s}-14)(\mathrm{s}-15)}=84 \\ & r_1=\frac{\Delta}{\mathrm{s}-a}=\frac{84}{21-13}=\frac{21}{2}\end{aligned}\)