Can you help me solve this problem using the Pythagorean Theorem

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?

Cynthia M. | UC Berkeley Educated Tutor with Patience and CreativityUC Berkeley Educated Tutor with Patience...

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First of all, you need to prove that the distances are all part of a right triangle. Cardinal directions such as north and east are perpendicular to each other on a compass. This proves that the angle formed between walk north and east is 90 degrees. As x and 2x+4 intersect at this 90 degree angle then it must be deduced that 2x+6 is the length of the hypotenuse. This is where we derive that in the Pythagorean theorem c is always the long hypotenuse so it must be that c=2x+6. It does not matter whether x is a or b because both parts are interchangeable.

So the equation states, let a=x, b=2x+4 and c=2x+6.

Plug these conditions into the Pythagorean Theorem and solve.