SOLUTION: This is the word problem that has gotten the best of me. Any help will be greatly appreciated. Ahmed has half of a treasure map, which indicates that the treasure is buried in

Question 883902: This is the word problem that has gotten the best of me. Any help will be greatly appreciated.
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?
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887) (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. If they share their information, then they can find x and save a lot of digging. What is x?
=============================
Draw the picture::
You have a circle with radius 2x+6
----------
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]
========
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)]
====================
Cheers,
Stan H.
----------------------
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
This is the word problem that has gotten the best of me. Any help will be greatly appreciated.
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?

**HINT: This scenario denotes a right-triangle, with a hypotenuse of 2x + 6, and legs of x, and 2x + 4.
After solving,
You can do the check!!
If you need a complete and detailed solution, let me know!!
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