Question

The diameter of the circumcircle of a triangle with sides $5$ cm, $6$ cm, $7$ cm, is?

• A. $\frac{3\sqrt{6}}{2}cm$
• B. $2\sqrt{6}cm$
• C. $\frac{35}{48}cm$
• D. none of these

Answer 1

The correct option is D none of these

Given that, $a=5$; $b=6$; $c=7$

We know that $s=\frac{a+b+c}{2}=\frac{5+6+7}{2}=\frac{18}{2}=9$
Therefore, $s=9$
now, $△=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{9(9-5)(9-6)(9-7)}$
$\Rightarrow △=6\sqrt{6}$
diameter of circumcircle=$2R=\frac{abc}{2△}=\frac{5\times 6\times 7}{2\times 6\sqrt{6}}=\frac{35}{2\sqrt{6}}$