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miller_intermediate_algebra_4e_ch1_3

Section 1.3 Applications to Geometry and Literal Equations 69 To write a verbal model, we might consider using the formula for the perimeter of a rectangle. However, the formula incorporates all four sides of the rectangle. The formula must be modified to include only one factor of the width. Verbal model aDistance around three sides b a 2 times the length b a 1 times the width 774 2(3x 2) x Mathematical equation Solve for x. Apply the distributive property. Combine like terms. Subtract 4 from both sides. Divide by 7 on both sides. 774 213x 22 x 774 6x 4 x 774 7x 4 770 7x 110 x x 110 Because x represents the width, the width of the corral is 110 ft. The length is given by Interpret the results. The width of the corral is 110 ft, and the length is 332 ft. Skill Practice 1. The length of Karen’s living room is 2 ft longer than the width.The perimeter is 80 ft. Find the length and width. Recall some important facts involving angles. • Two angles are complementary if the sum of their measures is • 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°. Solving an Application Involving Angles Example 2 Two angles are complementary. One angle measures 10° less than 4 times the other angle. Find the measure of each angle (Figure 1-3). 90°. 3x 2 or 311102 2 332 b P 2l 2w Avoiding Mistakes To check the answer to Example 1, verify that the three sides add to 774 ft. 110 ft 332 ft 332 ft 774 ft ✔ Answer 1. The length is 21 ft, and the width is 19 ft. 3x 2 3x 2 x x Figure 1-2 Let x represent the width. Label variables. Let 3x 2 represent the length. TIP: In Example 1, the length of the field is given in terms of the width. Therefore, we let x represent the width. Solution: Read the problem and draw a sketch (Figure 1-2). (4x 10)° x° Figure 1-3


miller_intermediate_algebra_4e_ch1_3
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