Question

Two persons start walking on roads that makes an angle of ${120}^{\circ }$ with each other. If they walk at the rate of 3 km/h and 2 km/h respectively. Find the distance between them after 4 hours.

• A. $4\sqrt{19}km$
• B. 5 km
• C. 7 m
• D. $8\sqrt{19}km$

Answer 1

The correct option is A $4\sqrt{19}km$

Distance after 4 hours = AB = c
$a=3\times 4=12;b=2\times 4=8$
and $\frac{a+b+c}{2}\Rightarrow \frac{12+8+c}{2}\Rightarrow (10+\frac{c}{2})Area=\sqrt{S(S-a)(S-b)(S-c)}Area=\frac{1}{2}absin{120}^{\circ }Area\Rightarrow 48\times \frac{\sqrt{3}}{2}=24\sqrt{3}$
As per question:
$24\sqrt{3}=\sqrt{(10+\frac{c}{2})(\frac{c}{2}-2)(2+\frac{c}{2})(10-\frac{c}{2})}$
On solving, we get $c=4\sqrt{19}km$