Question

ABC is a equilateral triangle of side 4cm.if R,r,and h are the circumradius, inradius,and altitude respectively, then$\frac{R+r}{h}$ is equal to?

• A. $4$
• B. $2$
• C. $1$
• D. $3$

Answer 1

The correct option is C $1$

Given that, $\Delta ABC$ is an equilateral triangle.
$\Rightarrow a=b=c=4$ and $A=B=C=\frac{\pi }{3}$
now, $s=6$ and $△=\frac{\sqrt{3}{a}^2}{4}=4\sqrt{3}$
From sine rule: $\frac{a}{\sin A}=2R$
$\Rightarrow R=\frac{4}{2\sin \frac{\pi }{3}}=\frac{4}{\sqrt{3}}$
now, $r=\frac{△}{s}=\frac{2}{\sqrt{3}}$
and $h=\frac{2△}{a}=\frac{2\times 4\sqrt{3}}{4}=\frac{6}{\sqrt{3}}$
Therefore, $\frac{R+r}{h}=1$
Ans: C