Q67 / 160 · AP EAMCET 2022 (05 Jul Shift 1) · Mathematics

In a $\triangle A B C$, if $r_1=36, r_2=18$ and $r_3=12$, then $s=$

  • A
    $6$
  • B
    $8$
  • C
    $16$
  • Correct answer
    D
    $36$

Solution

Given, $r_1=36, r_2=18$ and $r_3=12$ We know that, in a $\triangle A B C$ $\frac{1}{r}=\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}$ $\Rightarrow \frac{1}{r}=\frac{1}{36}+\frac{1}{18}+\frac{1}{12} \Rightarrow \frac{1}{r}=\frac{2+4+6}{72}$ $r=6$ Now, we know that, $\begin{aligned} & \Delta^2=r \cdot r_1 \cdot r_2 \cdot r_3=6 \times 36 \times 18 \times 12 \\ & \Delta^2=6^2 \times 6^2 \times 6^2\end{aligned}$ $\Delta=6 \times 6 \times 6=216$ Again we know that, $r=\frac{\Delta}{S}=\frac{216}{S}$ $\Rightarrow \quad S=\frac{216}{6}=36$

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

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