Q68 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Mathematics
In triangle $\mathrm{ABC}$, if $a=7, b=10, c=11$, then $\frac{\mathrm{R}}{r}=$
- A14
- B77
- C$\frac{24}{11}$
- Correct answerD$\frac{55}{24}$
Solution
$$
\begin{aligned}
& \text { } \mathrm{S}=\frac{7+10+11}{2}=14 \\
& \Delta=\sqrt{14(14-7)(14-10)(14-11)} \\
& =\sqrt{14 \times 7 \times 4 \times 3}
\end{aligned}
$$
We have
$$
\mathrm{R}=\frac{\mathrm{abc}}{4 \mathrm{D}} \text { and } \mathrm{r}=\frac{\Delta}{\mathrm{S}}
$$
$$
\begin{aligned}
& \therefore \frac{\mathrm{R}}{\mathrm{r}}=\frac{\mathrm{abc}(\mathrm{S})}{4 \mathrm{D}^2} \\
& =\frac{7 \times 10 \times 11 \times 14}{4 \times 14 \times 7 \times 4 \times 3}=\frac{55}{24}
\end{aligned}
$$
Hence, the correct answer is option: 'D'.