Question

The correct match for LIST-I from LIST-II
The area of a triangle ABC is 400$\sqrt{3}$

List-I	List-II
a) $s=20(2+\sqrt{3})$	1. $R=40$
b) $s-a=20\sqrt{3}$	2. $r=20(2\sqrt{3}-3)$
c) $r=10\sqrt{3}$	3. $S=40$
d) $abc=64000\sqrt{3}$	4. $r_1=20$

The correct match for LIST-I from LIST-II

• A. $a-2,b-4,c-3,d-1$
• B. $a-4,b-1,c-3,d-2$
• C. $a-1,b-2,c-4,d-3$
• D. $a-3,b-1,c-2,d-4$

Answer 1

The correct option is A $a-2,b-4,c-3,d-1$

$A$

$\Delta =400\sqrt{3}r=\frac{\Delta }{s}r=\frac{400\sqrt{3}}{20(2+\sqrt{3})}r=\frac{400\sqrt{3}}{20(2+\sqrt{3})}\times \frac{(2-\sqrt{3})}{(2-\sqrt{3})}r=20(2\sqrt{3}-3)$

$B$

$r_1=\frac{\Delta }{s-a}=\frac{400\sqrt{3}}{20\sqrt{3}}=20$

$C$

$10\sqrt{3}=\frac{400\sqrt{3}}{s}s=40$

$D$

$R=\frac{abc}{4\Delta }=\frac{64000\sqrt{3}}{4\left(400\sqrt{3}\right)}=40$

Option $A$ is correct.