Question

The area of the triangle whose sides are $6$ cm, $7$ cm and $11$ cm is given by $a\sqrt{b}$.

Find the value of $b-a$.

Answer 1

Area of a triangle whose sides (in cm) are $a,b$ and $c=\sqrt{s(s-a)(s-b)(s-c)}$,

where $s=\frac{a+b+c}{2}\Rightarrow s=\frac{6+7+11}{2}=12$
Area $=\sqrt{12(12-6)(12-7)(12-11)}=6\sqrt{10}$ c$m^2$

$\Rightarrow a\sqrt{b}=6\sqrt{10}$

$\Rightarrow b-a=10-6=4$