Section 2.5 Formulas and Applications from Geometry 139 450 = 6w Simplify. 450 6 = 6w 6 Divide each side by 6. 75 = w Simplify. So, the width of the soccer field is 75 yd. The length is 2(75) - 30 = 150 - 30 = 120 yd. 2d. The circumference of the inner circle of the Columbus Circle in New York City measures approximately 673 ft, and the circumference of the outer circle is approximately 1364 ft. Find the radius of the inner and outer circles. Find the area of the inner circle. Round all values to the nearest hundredth. Solution 2d. Since we know the circumference of each of the inner and outer circles, we use the circumference formula to find the radii. Circumference of inner circle Circumference of outer circle C = 2πr State the circumference formula. Replace the value of C with the given circumference. Divide each side by 2π. C = 2πr 673 = 2πr 1364 = 2πr 673 2π = 2πr 2π 1364 2π = 2πr 2π 673 2π 1364 2π = r = r 107.11 ≈ r Simplify. 217.09 ≈ r The radius of the outer circle is approximately 217.09 ft. The radius of the inner circle is approximately 107.11 ft. Now that we know the radius of the inner circle, we can find its area. A = πr2 State the area formula. A = π (107.11)2 Replace r with 107.11. A = π (11,472.5521) Simplify (107.11)2. A = 36,042.09 Multiply by π. So, the area of the inner circle is approximately 36,042.09 ft2. Student Check 2 Use the perimeter, area, or circumference formulas to solve each problem. a. The largest painting at the Louvre Museum is the Wedding at Cana by Veronese. Its perimeter is 1304 in. and its width is 262 in. Find its length and then the area of the painting. b. Find the length of the base of a triangle whose area is 10 ft2 and whose height is 4 ft. c. The length of the White House is 3 ft less than twice its width. If the perimeter of the White House is 507 ft, find its length and width. d. Find the area and circumference of the clock face on top of Big Ben in London if the diameter of the clock face is 23 ft. Rewriting Formulas The Fahrenheit-Celsius formula illustrated in Example 1b can be used to find Fahrenheit or Celsius values. When the Celsius temperature was given, we evaluated the formula to determine the corresponding Fahrenheit value because the formula was Objective 3 ▶ Solve formulas for a specified variable.
hendricks_beginning_algebra_1e_ch1_3
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