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I need help in seeing how to work this out. PLEASE

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?

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Gene G. | You can do it! I'll show you how.You can do it! I'll show you how.
5.0 5.0 (246 lesson ratings) (246)

Thomas is right.

From Castle rock, the northward leg of the right triangle is x paces.  The eastward leg from there is (2x+4) paces, and the straight line distance (the hypotenuse) is (2x+6) paces.  We can make a quadratic equation with this information.

As Thomas pointed out, the Pythagorean theorem states that the square of the hypotenuse is the sum of the squares of the legs:

a2 + b2 = c2

x2 + (2x+4)2 = (2x+6)2

Expand the squares and combine terms.

x2 + 4x2 + 16x + 16 = 4x2 + 24x + 36

x2 + 4x2 - 4x2 + 16x - 24x + 16 - 36 = 0

x2 - 8x - 20 = 0

We can factor this to get:

(x-10)(x+2) = 0

So x could be 10 or -2.  Negative 2 doesn't make sense in this situation, so:

x = 10.

Thomas W. | BS in Microbiology; grad student; 8+ years tutoring experienceBS in Microbiology; grad student; 8+ yea...
4.9 4.9 (348 lesson ratings) (348)


It can that expected that since the information given to one person is only a distance that is the hypotenuse, while the other person has the other two sides of the triangle, so the answer would be the  pythagorean theorem, where a2 + b2 = c2 where a= x, b= 2x+4, and c= 2x+6. Hope that helps.