I begin (2)

Geometry Level 1

In the above triangle ABC if $a=4,b=3,c=2,m=n=2.$

If the value of $p$ can be represented as $\frac{\sqrt{x}}{\sqrt{y}}$ for coprime positive integers $x,y$ , then find the value of $x+y$ .

1 solution

Siddharth Singh
Jun 19, 2015

We can use Stewart's theorem:

$a(p^{2}+mn)=b^{2}m+c^{2}n$

$4(p^{2}+4)=9*2+4*2=18+8=26$

$4p^{2}+16=26$

$p=\sqrt{\frac{10}{4}}=\sqrt{\frac{5}{2}}$

$x+y=5+2=7$