Question 788868
{{{drawing(300,200,-1,29,-2,13,
triangle(0,0,0,10,24,10),
rectangle(0,10,1,9),
locate(0.2,6,x),locate(10,10,2x+4),
locate(9.5,4,2x+6),
arrow(25,-1,25,7),locate(24.5,8,N),
locate(-1,-0.2,Castle),locate(4.5,-0.2,Rock),
locate(22,11,treasure)
)}}} {{{x^2+(2x+4)^2=(2x+6)^2}}} is our equation
 
Solving:
{{{x^2+(2x+4)^2=(2x+6)^2}}}
{{{x^2+(2x+4)^2=(2x+6)^2}}}
{{{x^2+(2x)^2+2*(2x)*4+4^2=(2x)^2+2*(2x)*6+6^2}}}
{{{x^2+4x^2+16x+16=4x^2+24x+36}}}
{{{x^2+16x+16=24x+36}}}
{{{x^2+16x+16-24x-36=0}}}
{{{x^2-8x-20=0}}}
{{{(x-10)(x+2)=0}}}
{{{x+2=0}}}--> {{{x=-2}}} does not make sense, because the x in "x paces to the north" should be a positive number
{{{x-10=0}}} --> {{{highlight(x=10)}}} is the only answer that makes sense.