Child Rearing Practices

In: Philosophy and Psychology

Submitted By Diane2351
Words 625
Pages 3
Pythagorean Quadratic
Diane Todd
MAT 221 Introduction to Algebra
Instructor Alicia Davis
September 29, 2013

Treasure hunts have always been a big deal in our home. Having raised five boys, anything to do with an adventure was exciting. Actually, this past June I planned one of my grandsons birthday parties around the theme of pirates and treasure hunting. I had never considered the math that went behind the maps in which I made up. Needless to say, when I saw the question entitled “buried treasure” in our math book, it brought back numerous memories. 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? Even though Ahmed’s half of the map does not tell him which direction the 2x + 6 paces should go, Ahmed can assume that his and Vanessa’s paces should end up in the same place. If I sketch out this scenario on paper, I see that I have a right triangle with 2x + 6 being the length of the hypotenuse, and 2x + 4 being the legs of the triangle. I now can use the Pythagorean Theorem to solve for x. The Pythagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse of c, these lengths have the relationship of a2 + b2 = c2. So if I put these measurements into the Pythagorean Theorem than I have the following:
(2x +6) = x + (2x +4) The original equation.
(2x + 6)2 = x2 + (2x + 4)2 The binominals into the Pythagorean Theorem.
(2x + 6)(2x + 6) = x2 + 4x2 +16x + 16
4x2 + 24x + 36 = 5x2 + 16x + 16 Combined all like terms.
-4x2 – 24x – 36 Subtract from both…...

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