Question

A triangle has sides of length $13,30$ and $37$. If the radius of the inscribed circle is $\frac{p}{q}$ (where p and q are coprime),then the value of $q^{p+3}$ is

• A. $2048$
• B. $4096$
• C. $1024$
• D. $512$

Answer 1

The correct option is B $4096$

The radius of incircle $=\sqrt{\frac{(s-a)(s-b)(s-c)}{s}}$

Now,

$S=\frac{37+13+30}{2}=40$

So, $r=\sqrt{\frac{(40-30)(40-37)(40-13)}{40}}r-\sqrt{\frac{10\times 3\times 27}{40}}r=\frac{9}{2}\frac{-p}{q}$

So, the value of $=q^{(p+3)}=2^{(q+3)}=2^{12}=4096$