Section 2.3 Formulas and Applications 77 3w – 5 w 2e. The length of a rectangle is 5 ft less than three times its width. If the perimeter is 150 ft, find the length and width of the rectangle. 3 times the width 5 less than Solution 2e. Let w represent the width. Then 3w - 5 represents the length. P = 2l + 2w Begin with the perimeter formula. 150 = 2(3w - 5) + 2w Replace l with 3w - 5. 150 = 6w - 10 + 2w Apply the distributive property. 150 = 8w - 10 Combine like terms. 150 + 10 = 8w - 10 + 10 Add 10 to each side. 160 = 8w Simplify. 160 8w = 8 8 Divide each side by 8. 20 = w Simplify. Check: 150 = 2(3w - 5) + 2w Begin with the original equation. 150 = 23(20) - 5 + 2(20) Replace w with 20. 150 = 2(60 - 5) + 40 Multiply. 150 = 2(55) + 40 Subtract inside the parentheses. 150 = 110 + 40 Multiply. 150 = 150 True So, the width is 20 ft and the length is l = 3w - 5 = 3(20) - 5 = 60 - 5 = 55 ft. Student Check 2 Use the perimeter, area, or circumference formulas to solve each problem. a. Find the area and perimeter of a rectangle whose length is 18 in. and whose width is 12 in. b. Find the area and circumference of a circle whose radius is 4 in. c. Find the area of a square whose perimeter is 12 ft. d. The London Eye in London, England, was the tallest Ferris wheel in the world until the Singapore Flyer was constructed. It has a diameter of 122 m (approximately 400 ft). What is the distance (in meters and feet) of one revolution around the London Eye? Use the value 3.14 for π. e. The width of a rectangle is 4 ft more than five times its length. If the perimeter of the rectangle is 428 ft, find the length and width of the rectangle. Other Formulas In Objective 2, we used formulas to find the area and perimeter of certain geometric shapes. Other important formulas deal with converting degrees Fahrenheit to degrees Celsius, calculating the amount of money in a savings account, and many more. Some of the formulas are shown. Compound Interest Formula (compounded annually) A = P (1 + r)t P: principal or amount invested r: annual interest rate (as a decimal) t: time of investment (in years) A: total amount saved Celsius-to-Fahrenheit conversion F = 9 5 C + 32 F: degrees Fahrenheit C: degrees Celsius 5 5 Objective 3 ▶ Use other formulas.
hendricks_intermediate_algebra_1e_ch1_3
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