Patricia Diggs
MAT 221 Introduction to Algebra
Instructor Bridget Simmons
May 12, 2013
Pythagorean Theorem: Finding Treasure
In this paper I will attempt to use the Pythagorean Theorem to solve the problem which reads 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 they can find x and save a lot of digging. What is x?
The Pythagorean Theorem states that in every right triangle with legs the length a and b and hypotenuse c, these lengths have the relationship of a2 + b2=c2.
a=x b=(2x+4)2 c=(2x+6)2 this is the binomials we will insert into our equation
x2+(2x+4)2=(2x+6)2 the binomials into the Pythagorean Theorem
x2+4x2+16x+16=24x36 the binomial squared. The 4x2can be subtracted out first
x2+16x+16=24x+36 now subtract 24x from both sides
x2+-8x+16=36 now subtract 36 from both sides
x2-8x-20=0 this is a quadratic equation to solve by factoring and using the
zero factor.
(x- )(x+ ) the coefficient of x2 is one (1). We can start with a pair of
parenthesis with an x each. We have to find two factors of -20
know that add up to -8. We know that since 20 is a negative
number we know that one will be a positive and one will be a
negative number. The two factors that will work are 2 and -10.
(x=-10)(x+2)=0 Use the zero factor property to solve each binomial, creating a
compound equation.
x=-2 or x=10...
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