Question 60821
Vanessa's portion tells us: "walk ‘x’ paces to the North, and then walk (2x + 4) paces to the East [from castle rock]" suggests a right-triangle with sides x and (2x+4).  So the distance from castle rock that you would walk if you went straight to the treasure is given by the pythagorean theorem:
{{{sqrt((2x+4)^2+x^2)}}}

Ahmed's portion says the distance from castle rock that you would walk if you went straight there is:

{{{2x+6}}}

So, set those two equal to each other and solve for x:

{{{sqrt((2x+4)^2+x^2)=2x+6)}}}
Square both sides:
{{{(2x+4)^2+x^2=(2x+6)^2}}}
{{{4x^2+16x+16+x^2=4x^2+24x+36}}}
{{{x^2-8x-20=0}}}
{{{(x-10)(x+2)=0}}}
Assuming x must be positive (otherwise the treasure map is quite misleading), the answer is:
{{{highlight(x=10)}}}