Question 883902
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?
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Draw the picture::
You have a circle with radius 2x+6
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Draw rectangle with side north = x and side right = 2x+4
Find the hypotenuse:
h = sqrt[x^2 + 4x^2+16x + 16]
h = sqrt[5x^2 + 16x + 16]
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Equate the radius and the hypotenuse and solve for "x":
2x+6 = sqrt(5x^2 + 16x + 16)
Square both sides to get: 
4x^2 + 24x + 36 = 5x^2 + 16x + 16
x^2 - 8x - 20 = 0
Solve:
x = [8 +- sqrt(16-4*-20)]/2
x = [8 +- sqrt(96)]/2
x = [8 +- 4sqrt(6)]/2
Positive solution:
x = [4 + 2sqrt(6)]
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Cheers,
Stan H.
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