Applied Problem 2 - Rebekah Unruh Honors Algebra I Problem...

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Rebekah Unruh Honors Algebra 9-27-07 I. Problem Description A nature conservancy group decides to construct a raised wooden walkway through a wetland area. To enclose the most interesting part of the wetlands, the walkway will have the shape of a right triangle with one leg 700 yd longer than the other and the hypotenuse 100 yd longer than the longer leg. Find the total length of the walkway. II. Math Concepts Because the problem involves a right triangle, the Pythagorean Theorem, “the square of the length of leg a added to the square of the length of leg b is equal to the square of the length of the hypotenuse c ,” will be used. Symbolically this is written as a ² + b ² = c ². Substituting values in this formula will result in a quadratic equation that must be solved. III. Construction of the Mathematical Model Both legs a and b and the hypotenuse c are unknown in the problem. To reduce the unknowns to a single variable, x can be substituted for leg a . From the problem description we know that leg b
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