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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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2 Answers

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.

Cathie,

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.