Answered: Vincent wants to build a rectangular…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Vincent wants to build a rectangular vegetable garden with an area of 600 square feet. He has 100 feet of fence and wants to use all the fence to completely enclose the garden. He correctly uses the equation x(50−x)=600 to model the scenario, where x represents the length, in feet, of one side of the garden. To find the value of x, he correctly rewrites the equation in standard form as x2−50x+600=0. Which of the following statements best describes how to calculate the dimensions of the garden?

Answer A: The equation is equivalent to open parenthesis, x plus 20, close parenthesis, times, open parenthesis, x plus 30, close parenthesis, equals 0 , and it has two positive solutions, x equals 20 and x equals 30 , so the garden has dimensions of 20 feet by 30 feet.

Answer B: The equation is equivalent to open parenthesis, x minus 20, close parenthesis, times, open parenthesis, x minus 30, close parenthesis, equals 0 , and it has two positive solutions, x equals 20 and x equals 30 , so the garden has dimensions of 20 feet by 30 feet.

Answer C: The equation is equivalent to open parenthesis, x plus 20, close parenthesis, times, open parenthesis, x minus 30, close parenthesis, equals 0 , and it has one positive solution, x equals 30 . When one side of the garden has a length of 30 feet, the other side has a length of 20 feet, so the garden has dimensions of 20 feet by 30 feet.

Answer D: The equation is equivalent to open parenthesis, x minus 20, close parenthesis, times, open parenthesis, x plus 30, close parenthesis, equals 0 , and it has one positive solution, x equals 20 . When one side of the garden has a length of 20 feet, the other side has a length of 30 feet, so the garden has dimensions of 20 feet by 30 feet.

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