Q66 / 160 · AP EAMCET 2024 (22 May Shift 2) · Mathematics

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

  • A
    $\frac{23}{2}$
  • Correct answer
    B
    $\frac{21}{2}$
  • C
    $\frac{25}{2}$
  • D
    $\frac{26}{3}$

Solution

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

Hence, the correct answer is option: 'B'.

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