Question 211667
Obviously, the 2 halves of the map must indicate that the treasure is in the same location


With Ahmed’s instructions that the treasure is (2x + 6) paces from Castle Rock, a diagram would indicate that the distance from Castle Rock, which is at a southern point, to the treasure spot, would form the hypotenuse of a right triangle - a hypotenuse that goes from south to the north-east (I wish I could draw the diagram to make it much clearer).


Based on Vanessa’s half, the “x” paces from Castle Hill, in a northern direction, and the (2x + 4) paces in an eastern direction, would form the legs of the right triangle.


Therefore, we would have a right triangle that would have legs of “x” and “(2x + 4),” and a hypotenuse of (2x + 6) paces. Using the Pythagorean formula, we will then have:

{{{x^2 + (2x + 4)^2 = (2x + 6)^2}}}

{{{x^2 + 4x^2 + 16x + 16 = 4x^2 + 24x + 36}}}

{{{x^2 + 4x^2 - 4x^2 + 16x - 24x + 16 - 36 = 0}}}

{{{x^2 - 8x - 20 = 0}}}

(x – 10)(x + 2) = 0

So, x – 10 = 0, or x + 2 = 0 -------> x = 10, or – 2 (ignore as measurement CANNOT be negative)

Therefore, {{{highlight_green(x = 10)}}}