Pythagorean Quadratic Treasure Hunters

Pythagorean Quadratic Treasure Hunters
Introduction to Algebra

Treasure Hunters
Ahmed and Vanessa both have possession of one half of a complete treasure map. Ahmed’s map shows the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa’s map shows the treasure buried at x paces to the north and 2x + 4 paces to the east. When the two combine information, the location of the buried treasure is going to be a lot easier to find and they can share in the booty loot that they discover.
Castle Rock is the lowest left point of the hypotenuse and at the bottom of the left leg and the treasure is at the furthest right point of the right leg. To factor the equation we start with the following,
X2+(2x + 4)2 = (2x+6)2 Using the Pythagorean Theorem, a2+2ab+b2 i get a compound
X2 +(4x216x+16)=4x2+24x+36 equation. It is then necessary to simplify using the quadratic
5x2+16x+16=4x2+24x+36 equation ax2-bx+c=0 so that I can factor.
(x2+2)(x-10)=0 everything is set to zero for the zero factor X = 10 solve for x

Plugging the x value for a, b, and c to the legs or the hypotenuse and what this does is it gives me the equation of how many paces it is to the treasure
A= 10
B=2(10)+4 = 20+4 = 24
C=2x+6 = 2(10)+6 = 26
In conclusion, castle rock is located at the bottom left of a right hand triangle, and the treasure is 26 paces northeast of Castle Rock. But, another way to find it is to travel 10 paces to the north and 24 paces to east. The operation and evaluation of equation allows for an efficient way to find the buried treasure without digging to many holes.

Reference:
Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing.