Explanation Given: The length and width of the room is 15 ft and 20 ft respectively. Also, the area of the rug is 234 ft 2 . Formula used: The length and width of the room as l and b respectively. The area of the room is given by. A room = l b And, The quadratic formula to solve the quadratic equation a x 2 + b x + c . x = − b ± b 2 − 4 a c 2 a Here, a , and b are the coefficient of x 2 and x respectively. Also, c represents the constant term. Calculation: Consider the length and width of the room as l and b respectively. Then, the area of the room. A room = l b Substitute 20 ft for l , and 15 ft for b . A room = ( 20 ft ) ( 15 ft ) = 300 ft 2 The area of the rug is 234 ft 2 . Thus, calculate the remaining area of the strip around the rug. A remaining strip = A room − A rug Substitute 300 ft 2 for A room , and 234 ft 2 for A rug . A remaining strip = 300 ft 2 − 234 ft 2 = 66 ft 2 Now, consider the rectangle A B C D as the room and E F G H as the rug. Then, the area between the room and the rug denotes the area of the remaining strip. Draw the sketch of the rug surrounded by flooring. Four rectangles formed by the remaining strip. The two rectangles will be on the left and right side. Also, the two rectangles will be on the top and bottom side. Draw the diagram of the four rectangles with different colors. The two rectangles on the left and the right sides have equal area. The rectangle on the left side has an area of ( 15 × w ) . Thus, calculate the area of the rectangles at the left and right side as shown by the shaded region in Figure 2. A rectangles at the left and right side = 2 ( 15 × w ) = 30 w Similarly, the area on the top and bottom sides have equal area. The rectangle on the top side has an area of ( ( 20 − 2 w ) × w ) . Thus, calculate the area of the rectangles at the top and bottom sides as shown by the shaded region in Figure 2. A rectangles at the top and bottom side = 2 ( ( 20 − 2 w ) × w ) = 40 w − 4 w 2 Now, the area of all the rectangles on the left and right side, and on the top and bottom side of the rectangle is equal to the area of the remaining strip

Mathematical Ideas (13th Edition) - Standalone book

13th Edition

ISBN: 9780321977076

Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren

Publisher: PEARSON

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Chapter 7.7, Problem 55E

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Chapter 7.7, Problem 54E

Chapter 7.7, Problem 56E

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Mathematical Ideas (13th Edition) - Standalone book

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Solve each equation. 6. Ch. 7.1 - Prob. 7E Ch. 7.1 - Solve each equation. 4x+5x8+4=6x4 Ch. 7.1 - Solve each equation. 9. Ch. 7.1 - Prob. 10E

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The width of the strip if the area of the rug is 234 ft 2 .

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