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Pythagorean Quadrant

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Pythagorean Quadratic
Melissa Hernandez
MAT221: Introduction to Algebra
Instructor Srabasti Dutta
August 4, 2014

Pythagorean Quadratic
Ever since I can remember when I was a little girl full of curiosity, I enjoyed the thought of finding a buried treasure and thus set out on treasure hunts with my sisters. Depending on how big your imagination is, you can take yourself to exotic locations, around town, or in your very own backyard. Finding buried treasures is a fun activity to do on your own or in a group. In this activity, we will be finding a buried treasure near Castle Rock with Ahmed and Vanessa. The assignment reads;
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? (Dugopolski, 2012, p. 371)
In this problem, we will use the Pythagorean Theorem which says that when a triangle has a right angle of 90 degrees, and squares are made on each of the three sides, then the biggest square has the exact same area as the other two squares put together. The Pythagorean Theorem can be written as: a^2 + b^2 = c^2 with “c” being the longest side or otherwise called the hypotenuse of the triangle, and “a” and “b” are the other two sides of the triangle. In a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. We let a = x, and b = 2x + 4, so that c = 2x + 6. Then we begin the equation: x^2 + (2x + 4)^2 = (2x + 6)^2 | The binomials are placed into the Pythagorean Theorem. | x^2 + 4x^2 + 16x + 16 = 4x^2 + 24x + 36 | The binomials are squared | -4x^2

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