Explanation Given Information: A border of uniform width is built around a rectangular garden that measures 16 ft by 20 ft. The area of the border is 160 ft 2 . Formula used: The following method is used, Step 1. Make a drawing on the basis of given information. Step 2. Translate the given information into the form of equation. Step 3. Solve the equation. Step 4. State the result. Calculation: Make a diagram on the basis of given information, Let x = width of the border, So, 20+2 x = length of the rectangular garden with border. 16+2 x = width of the rectangular garden with border. First, calculate the area of the rectangular garden as follows, 16 ft × 20 ft = 320 ft 2 It is given that the area of the border is 160 ft 2 so, The area of the rectangular garden with border is, 320 ft 2 + 160 ft 2 = 480 ft 2 Also, the area of the rectangular garden with border is, ( 20 + 2 x ) × ( 16 + 2 x ) = 480 ft 2 Solve this equation for x , ( 20 + 2 x ) × ( 16 + 2 x ) = 480 320 + 40 x + 32 x + 4 x 2 = 480 4 x 2 + 72 x + 320 − 480 = 0 4

Bundle: Elementary Technical Mathematics, Loose-leaf Version, 12th + WebAssign Printed Access Card, Single-Term

12th Edition

ISBN: 9781337890199

Author: Dale Ewen

Publisher: Cengage Learning

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Question

Chapter 11.3, Problem 13E

To determine

To calculate: The width of the border which is built around a rectangular garden that measures 16 ft by 20 ft. The border is of uniform width and the area of the border is 160 ft².

Expert Solution & Answer

Chapter 11 Solutions

Bundle: Elementary Technical Mathematics, Loose-leaf Version, 12th + WebAssign Printed Access Card, Single-Term

Ch. 11.1 - Solve each equation: x2+x=12 Ch. 11.1 - Solve each equation: x23x+2=0 Ch. 11.1 - Solve each equation: x2+x20=0 Ch. 11.1 - Prob. 4E Ch. 11.1 - Solve each equation: x22=x Ch. 11.1 - Solve each equation: x215x=54 Ch. 11.1 - Solve each equation: x21=0 Ch. 11.1 - Solve each equation: 16n2=49 Ch. 11.1 - Solve each equation: x249=0 Ch. 11.1 - Prob. 10E

Knowledge Booster

The width of the border which is built around a rectangular garden that measures 16 ft by 20 ft. The border is of uniform width and the area of the border is 160 ft 2 .

Solution Summary: The author explains how to calculate the width of the border built around a rectangular garden.

To calculate: The width of the border which is built around a rectangular garden that measures 16 ft by 20 ft. The border is of uniform width and the area of the border is 160 ft².

Chapter 11 Solutions

The width of the border which is built around a rectangular garden that measures 16 ft by 20 ft. The border is of uniform width and the area of the border is 160 ft 2 .

Solution Summary: The author explains how to calculate the width of the border built around a rectangular garden.

To calculate: The width of the border which is built around a rectangular garden that measures 16 ft by 20 ft. The border is of uniform width and the area of the border is 160 ft2.

Chapter 11 Solutions

To calculate: The width of the border which is built around a rectangular garden that measures 16 ft by 20 ft. The border is of uniform width and the area of the border is 160 ft².