Question 666371: Buried treasure. Ahmed has half of a treasure map,which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of digging. What is x?
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! The directions form a right triangle with legs of x and (2x+4) and a hypotenuse of (2x+6). Use Pythy's theorem
(1) (2x+6)^2 = x^2 + (2x+4)^2 and get
(2) 4x^2 + 24x +36 = x^2 + 4x^2 +16x +16 or
(3) x^2 -8x -20 = 0 which factors to
(4) (x-10)(x+2) = 0
Choosing the positive root of 10 we have x = 10
Is this correct? Let's check.
Is ((2*10+6)^2 = 10^2 + (2*10+4)^2)?
Is (26^2 = 100 + 24^2)?
Is (676 = 100 + 576)?
Is (676 = 676)? Yes
Answer: the value of x is 10 paces, and the treasure is 10 paces north then 24 paces east of Castle Rock.
Q. Is this the Castle Rock in the UP of MI?
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