SOLUTION: Question: 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

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Question 788868: Question:
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?

On your scratch paper, draw a diagram which includes the location of Castle Rock and the dimensions of a triangle with the given number of paces. Seeing the relationship of the sides and where the right angle is will help you know how to apply the Theorem. You may include the diagram in your paper but are not required to do so.
Write the equation first by inserting the given binomials into the Pythagorean Theorem. Once you have your equation written, solve it using one of the methods of factoring. Show all steps.




Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B%282x%2B4%29%5E2=%282x%2B6%29%5E2 is our equation

Solving:
x%5E2%2B%282x%2B4%29%5E2=%282x%2B6%29%5E2
x%5E2%2B%282x%2B4%29%5E2=%282x%2B6%29%5E2
x%5E2%2B%282x%29%5E2%2B2%2A%282x%29%2A4%2B4%5E2=%282x%29%5E2%2B2%2A%282x%29%2A6%2B6%5E2
x%5E2%2B4x%5E2%2B16x%2B16=4x%5E2%2B24x%2B36
x%5E2%2B16x%2B16=24x%2B36
x%5E2%2B16x%2B16-24x-36=0
x%5E2-8x-20=0
%28x-10%29%28x%2B2%29=0
x%2B2=0--> x=-2 does not make sense, because the x in "x paces to the north" should be a positive number
x-10=0 --> highlight%28x=10%29 is the only answer that makes sense.