34 Chapter 1 Real Numbers and Algebraic Expressions ������������������������ The skills of simplifying numerical expressions, evaluating algebraic expressions or equations, and expressing relationships mathematically will be used in the context of real-life situations. One of the specific applications deals with calculating the perimeter of polygons. Polygons are two-dimensional closed shapes made up of straight lines, such as triangles, squares, rectangles, trapezoids, and the like. ������������������������ Perimeter of a Polygon The perimeter of a polygon is the total distance around the outside of the polygon. For example, the perimeter of a rectangular yard with width 100 ft and length 250 ft is P = 100 + 250 + 100 + 250 P = 700 So, the perimeter is 700 ft. �� ������������������������ ������������������ Solve each problem. 100 ft 250 ft 6a. If $5000 is invested in a savings account that earns 6% annual interest for 3 yr, the total amount saved is given by the equation. Amount saved = 5000(1.06)3 Find the amount that would be saved. Solution 6a. Simplifying the expression on the right side of the equation gives us that Amount saved = 5955.08 So, in 3 yr, a total of $5955.08 will be in the account. 6b. After renovations in 2010, the Michigan Stadium at the University of Michigan in Ann Arbor, Michigan, became the largest football stadium in the United States with a seating capacity of 108,000. The football field is in the shape of a rectangle. The perimeter P of a rectangle is the sum of 2 times its length and 2 times its width. i. Write an equation that denotes the perimeter of a rectangle, where l is the length and w is the width. ii. If the football field has a length of 360 ft and a width of 160 ft, what is the field’s perimeter? Solution 6b. i. The equation that represents the perimeter is P = 2l + 2w. ii. P = 2l + 2w Use the relationship defi ned in part (i). P = 2(360) + 2(160) Replace l with 360 and w with 160. P = 720 + 320 Simplify each product. P = 1040 Add. The perimeter of the football field is 1040 ft. 100 ft 250 ft Objective 6 ▶ Solve application problems.
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