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In a $\triangle A B C$, if $a=4 \mathrm{~cm}, b=6 \mathrm{~cm}$ and $c=8 \mathrm{~cm}$ then $r$ equals
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Verified Answer
The correct answer is:
$\sqrt{\frac{5}{3}}$
If $a=4 \mathrm{~cm}, b=6 \mathrm{~cm}$ and $c=8 \mathrm{~cm}$ then, $2 s=a+b+c$
$\mathrm{s}=9 \mathrm{~cm}$
But, $\Delta=\sqrt{s(s-a)(s-b)(s-c)}$ $\quad$ [by Heron's formula]
$=\sqrt{9 \times 5 \times 3 \times 1}$
so, $\quad r=\frac{\Delta}{s}$
or, $\quad r=\frac{3 \sqrt{15}}{9}$
or, $\quad r=\frac{\sqrt{15}}{3} \mathrm{~cm}$
or, $\quad r=\sqrt{\frac{5}{3}} \mathrm{~cm}$
$\mathrm{s}=9 \mathrm{~cm}$
But, $\Delta=\sqrt{s(s-a)(s-b)(s-c)}$ $\quad$ [by Heron's formula]
$=\sqrt{9 \times 5 \times 3 \times 1}$
so, $\quad r=\frac{\Delta}{s}$
or, $\quad r=\frac{3 \sqrt{15}}{9}$
or, $\quad r=\frac{\sqrt{15}}{3} \mathrm{~cm}$
or, $\quad r=\sqrt{\frac{5}{3}} \mathrm{~cm}$
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