Pythagorean Quadratic
Pythagorean Quadratic
Member
MAT 222 Introduction to Algebra
Instructor Yvette Gonzalez-Smith
August 04, 2013
Pythagorean Quadratic The Pythagorean Theorem is an equation that allows a person to find the length of a side of a right triangle, as long as the length of the other two sides is known. The theorem basically relates the lengths of three sides of any right triangle. The theorem states that the square of the hypotenuse is the sum of the squares of the legs. It also can help a person to figure out whether or not the triangle is a right triangle or not, as long as the length of the other two sides are given (The Pythagorean Theorem, 1991-2012). This week’s assignment was found on page 371; it is problem number 98, called “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? Although we were not given a direction for Ahmed’s half of the map, we figure that his and Vanessa’s paces will end up in the same place. I have drawn a diagram on a piece of scratch paper, which includes the location of Castle Rock, and the dimensions of a triangle with the given number of paces. According to the Pythagorean Theorem, right triangles with legs the length of a and b, have a hypotenuse of c, are related to one another as I will let a = x, b = 2x+4, and c = 2x+6. Now, I will use the theorem in order to solve the equation. I have plugged the binomials into the equation for the theorem. Using the FOIL method, I have performed the necessary multiplication; squaring a number is
Member
MAT 222 Introduction to Algebra
Instructor Yvette Gonzalez-Smith
August 04, 2013
Pythagorean Quadratic The Pythagorean Theorem is an equation that allows a person to find the length of a side of a right triangle, as long as the length of the other two sides is known. The theorem basically relates the lengths of three sides of any right triangle. The theorem states that the square of the hypotenuse is the sum of the squares of the legs. It also can help a person to figure out whether or not the triangle is a right triangle or not, as long as the length of the other two sides are given (The Pythagorean Theorem, 1991-2012). This week’s assignment was found on page 371; it is problem number 98, called “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? Although we were not given a direction for Ahmed’s half of the map, we figure that his and Vanessa’s paces will end up in the same place. I have drawn a diagram on a piece of scratch paper, which includes the location of Castle Rock, and the dimensions of a triangle with the given number of paces. According to the Pythagorean Theorem, right triangles with legs the length of a and b, have a hypotenuse of c, are related to one another as I will let a = x, b = 2x+4, and c = 2x+6. Now, I will use the theorem in order to solve the equation. I have plugged the binomials into the equation for the theorem. Using the FOIL method, I have performed the necessary multiplication; squaring a number is
References: Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing Polynomials. (2013). Retrieved from http://www.mathsisfun.com/algebra/polynomials.html The Pythagorean Theorem. (1991-2012). Retrieved August 4, 2013, from the Pythagorean Theorem website: http://www.purplemath.com/index.htm