SOLUTION: I need to figure out how to solve this problem step by step. Please. "Buried treasure. Ahmed has half of a treasure map,which indicates that the treasure is buried in the desert

Question 763101: I need to figure out how to solve this problem step by step. 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?" It says to write the equation first by inserting the given
binomials into the Pythagorean Theorem. I am supposed to base it off the
dimensions of a right triangle.I have no idea how to do this problem. Please
help if possible. Thank you''.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
"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?"
:
Draw this right triangle out and it will make sense to you
:
Start with a point called "Castle Rock"
Draw a line due north (up) and label it x
Draw another line from this point, due east (to the right) label (2x+4)
At the end of this line is the treasure.
Now from Castle Rock draw a line directly to the treasure
label this (2x+6), this is the hypotenuse of the right triangle
:
Pythag
x^2 + (2x+4)^2 = (2x+6)^2
FOIL
x^2 + 4x^2 + 16x + 16 = 4x^2 + 24x + 36
Combine like terms 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
The positive solution is all we want here
x = 10
:
:
We can find the actual paces now and check our work by using pythag
10 paces north
2(10)+4 = 24 paces east to the treasure
Castle rock is 2(10)+6 = 26 paces to the treasure
:
See is that works with a calc; enter results: 26!
:
Did this make sense to you? Any questions? C
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