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?
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.