Problema Solution
Buried Treasure. Amhed has half of a treasure map that indicates the treasure is buried in the desert 2x+6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates to find the treasure, one must get to Castle Rock, walk x paces to the north, then walk 2x+4 paces to the east. If they share their information, then they can find x, and save a lot of diffing. What is x?
Answer provided by our tutors
a = x
b = 2x + 4
c = 2x + 6
a^2 + b^2 = c^2
so we have:
x^2 + (2x+4)^2 = (2x+6)^2
FOIL
x^2 + 4x^2 + 16x + 16 = 4x^2 + 24x + 36
Combine on the left
x^2 + 4x^2 - 4x^2 + 16x - 24x + 16 - 36 = 0
x^2 - 8x - 20 = 0
Factors to
(x-10)(x+2) = 0
positive solution
x = 10
See if this is true?
10^2 + 24^2 = 26^2
100 + 576 = 676, it is