# Pythagorean Quadratic

Pythagorean Quadratic

MAT 221: Introduction to Algebra

Pythagorean Quadratic

The Pythagorean Theorem was termed after Pythagoras, who was a well-known Greek philosopher and mathematician, and the Pythagorean Theorem is one of the first theorems identified in ancient civilizations. “The Pythagorean theorem says that in any right triangle the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse” (Dugopolski, 2012, p. 366 para. 8). For this reason, many builders from various times throughout history have used this theorem to assure that their foundations were laid out with right angles. In this assignment, we will use the example of locating a treasure using two different treasure maps as the two points needed to determine how many paces it will take to find the exact location to start digging for treasure. For this assignment, we are given instructions to solve problem number 98 from page 371 in Elementary and Intermediate Algebra, which states that Ahmed’s treasure map specifies that the treasure can be found 2x +6 steps from Castle Rock and Vanessa’s half indicates to walk x steps heading north, then 2x + 4 steps toward the east (Dugopolski, 2012). We need use the Pythagorean Theorem to figure out what variable x would be if they were to work together and combine their information. The Pythagorean Theorem indicates that a right triangle has legs with the length of a and b and the longest side of the triangle, the hypotenuse, as the length of c. Thus, the relationship with these lengths is the short equation of a2 + b2 = c2 (Dugopolski, 2012). Let a = x

Let b = 2x + 4

Let c = 2x + 6

〖x 〗^2+ 〖(2x + 4)〗^2= 〖(2x + 6)〗^2Add the binomials to the Pythagorean Theorem. 〖x 〗^2+( 〖4x 〗^2)/( 〖-4x 〗^2 )+ 16x + 16 = 〖4x〗^2/〖-4x 〗^2 + 24x + 36 First, subtract the 4x2 on each side of equation and then square the binomials. 〖x 〗^2+16x/(-24x)+16=24x/(-24x)+36Subtract 24x on each side of equation. 〖x...

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