Question 255106: Thank you for your help, question is:
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, 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 east.
If they share their info, then they can find x and save a lot of digging, what is x ?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! the treasure is buried in the desert 2x+6 paces from castle rock.
Vanessa has the other half, 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 east.
:
From the description it is apparent that we have a right triangle where:
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
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