Algebra has been around for many years. Some people feel there is no use for algebra in the real world. There are those who feel it is a waste of time because only certain professions really use it. However, algebra is used in many ways which can relate to everyday situations. Algebra truly is a part of our everyday life and there really is no escaping it. This week, we are asked to solve a problem using the Pythagorean Theorem. The Pythagorean Theorem is a relation in geometry among the three sides of a right triangle.
The Theorem reveals that the square of the hypotenuse is equal to the sum of the squares of the other two sides. This information can provide useful information and save lots of time and aggravation. People in the construction business find this information quite helpful because it allows them to build a sound structure. Architects and those in the engineering profession also need this information and apply it to their everyday tasks. All three of these situations really do occur daily for many people and it is extremely important to be able to figure these things out.
On page 371 of our text, Elementary and Intermediate Algebra, question #98 tells us, “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).
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Even though Ahmed’s half of the map does not indicate which direction the paces 2x+6 should go, he can surmise his paces and Vanessa’s paces would end up in the same spot. On a piece of scratch paper, I sketched the information out. The information provided shows me a right triangle is formed with 2x+6 being the hypotenuse, x being one of the sides and 2x+4 being the other side of the triangle. Since a right triangle has been formed, we use the Pythagorean Theorem to solve for x. 2x+6 x 2x+4 Again, the Pythagorean Theorem tells us with every right triangle the length of the legs, a and b, and the hypotenuse, c, the lengths are a^2+b^2 = c^2.
With that being said, I start with a pair of parentheses with an x in each one; (x – )(x + ).
Since 20 is negative, there will be one positive and one negative in the binomials. I need two factors of 20 which when multiplied together are -20 and when added together are -8. -10 and 2 work because when multiplied together equals -20 and 2+(-10) = -8. (x – 10)(x + 2) = 0Use the zero factor to solve for each binomial. x – 10 = 0 or x +2 = 0Create a compound equation. +10 +10 -2 -2Solve for x using the rules. x = 10 or x = -2Here are the possible solutions for the equation.
Since we cannot have negative paces, -2 will simply not work. This leaves x = 10 as the appropriate number of paces. The treasure lies 10 paces to the north and 2x + 4 = 2(10)+4=24 paces east of Castle Rock, or 2x + 6 = 2(10)+6=26 paces straight from Castle Rock. Finding out how many paces are needed to find buried treasure is just one of the many uses of the Pythagorean Theorem in algebra. Our world has valid uses for this ancient form of mathematics. Many people do not realize just how useful and necessary algebra is. Architects, engineers and construction contractors have very valid uses for algebra.
Algebra allows them to plan, layout and build sound structures. Knowing how to use the Theorem allows contractors and engineers to build perfect structures, know just how much of the materials they would need and keep the building process on track. This week’s assignment has showed how important algebra is and how it can be applied to real world situations. Algebra is not easy for everyone to grasp, but it definitely serves a useful purpose. Reference Dugopolski, M. (2012).
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It is critical that people take responsibility for solving problems that affect their community so that everyone will have a better world to live in. It is lucid through several examples from literature such as 1984 and historical figures such as Rosa Parks and Peter Benenson that people must take responsibility to solve problems in their communities. In the novel 1984 by George Orwell, the main ...
Elementary and intermediate algebra (4th ed. ).
New York, NY: McGraw-Hill Publishing.
