76 Chapter 2 Linear Equations and Inequalities in One Variable Solution 2a. Perimeter Area P = 2l + 2w A = lw Begin with the appropriate formula. P = 2(5) + 2(12) A = (5)(12) Replace l with 5 and w with 12. P = 10 + 24 A = 60 Simplify. P = 34 The perimeter of the rectangle is 34 ft and the area of the rectangle is 60 ft2. 2b. What is the circumference and area of a circle whose radius is 6 cm? Solution 2b. Substitute the value of the radius in the circumference and area formulas. Circumference Area C = 2πr A = πr 2 Begin with the appropriate formula. C = 2π(6) A = π(6)2 Replace r with 6. C = 12π A = 36π Simplify. The circumference of the circle is 12π cm and the area is 36π cm2. 2c. The Singapore Flyer was the largest operating Ferris wheel in the world in the year 2008. It has a diameter of 150 m (approximately 492 ft). What is the distance of one revolution of the Ferris wheel? Find the distance in meters and feet. Use the value 3.14 for π. Solution 2c. To find the distance of one revolution, we must find the circumference of a circle whose diameter is 150 m, or 492 ft. C = πd = (3.14)(150) = 471 C = πd = (3.14)(492) = 1544.88 The distance traveled one time around the Singapore Flyer is approximately 471 m or 1544.88 ft. 2d. What is the height of a triangle whose area is 16 ft2 and whose base is 8 ft? Solution 2d. We know the area, A = 16, and the base, b = 8, of the triangle, so we substitute these into the area formula and solve for h. A = 1 2 bh Begin with the area formula. 16 = 1 2 (8)h Substitute the values of A and b. 16 = 4h Multiply on the right side. 16 4h = Divide each side by 4. 4 4 4 = h Simplify. So, the height of the triangle is 4 ft. Check: We can verify the solution by substituting h = 4 in the area formula. We get A = 1 2 (8)(4) = 1 2 (32) = 16. 12 ft 5 ft 6 cm h 8 ft
hendricks_intermediate_algebra_1e_ch1_3
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