Question 737245: 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? help me set it up please .
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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.
:
draw this out and you can see a right triangle with:
x = one leg
(2x+4) = another leg
(2x+6) = the hypotenuse
therefore using Pythagoras:
x^2 + (2x+4)^2 = (2x+6)^2
FOIL
x^2 + 4x^2 + 8x + 8x + 16 = 4x^2 + 12x + 12x + 36
5x^2 + 16x + 16 = 4x^2 + 24x + 36
combine like terms in the left
5x^2 - 4x^2 + 16x - 24x + 16 - 24x = 0
a quadratic equation
x^2 - 8x - 20 = 0
Factor to:
(x-10)(x+2) = 0
the positive solution
x = 10
:
Walk 10 paces north, 24 paces east, that point will be 26 paces from C.R.
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