2. Geometry Applications In Section R.4, we presented numerous facts and formulas related to geometry. Sometimes these are needed to solve applications in geometry. Solving a Geometry Application Involving Perimeter Example 3 The length of a rectangular lot is 1 m less than twice the width. If the perimeter is 190 m, find the length and width. Solution: Step 1: Read the problem. Let x represent the width of the rectangle. Step 2: Label the unknowns. Then represents the length. Step 3: Write the formula for perimeter. Step 4: Write an equation in terms of x. Step 5: Solve for x. 2x 1 P 2l 2w 190 212x 12 21x2 190 4x 2 2x 190 6x 2 192 6x 32 x The width is The length is Step 6: Interpret the results and write the answer in words. x 32. The width of the rectangular lot is 32 m and the length is 63 m. Recall some facts about angles. • Two angles are complementary if the sum of their measures is 90° . • Two angles are supplementary if the sum of their measures is 180° . • The sum of the measures of the angles within a triangle is 180° . • The measures of vertical angles are equal. 2x 1 21322 1 63. 192 6 6x 6 x 2x 1 166 Chapter 2 Linear Equations and Inequalities Skill Practice 4. The length of a rectangle is 10 less than twice the width. If the perimeter is 178, find the length and width. Classroom Example: p. 170, Exercise 46 Answer 4. The length is 56, and the width is 33.
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