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06 Jan 2025, 09:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (00:52) correct
25% (00:51) wrong based on 4 sessions
History
Date
Time
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In the figure, diagonal BD of square ABCD is 3. What is the perimeter of the square?
A. 4.5
B. 12
C. 3 \(\sqrt{2}\)
D. 6 \(\sqrt{2}\)
E. 12 \(\sqrt{2}\)
Attachment:
11.jpg [ 9.53 KiB | Viewed 375 times ]
11 Jan 2025, 01:16
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OE
Since this diagram has been drawn to scale, you can trust it. The sides of the square appear to be about two thirds as long as the diagonal, so assume that each side is about 2. Then the perimeter is about 8. Which of the choices is approximately 8? Certainly not A or B. Since \(\sqrt{2} \) nearly equals 1.4, Choices C, D, and E are approximately 4.2, 8.4, and 12.6, respectively. Clearly, the answer must be D.
Direct mathematical solution. Let s be a side of the square. Then since BCD is a 45-45-90 right triangle, \(s=\frac{3}{\sqrt{2}}\) \(= \frac{3\sqrt{2}}{2}\), and the perimeter of the square is 4s= \(\frac{3\sqrt{2}}{2}\) \(6 \sqrt{2}\).
Remember the goal of this book is to help you get credit for all the problems you know how to do, and, by using the TACTICS, to get credit for many that you don’t know how to do. Example 5 is typical. Many students would miss this question. You, however, can be sure that you will answer it correctly, even if you don’t remember how to solve it directly
Since this diagram has been drawn to scale, you can trust it. The sides of the square appear to be about two thirds as long as the diagonal, so assume that each side is about 2. Then the perimeter is about 8. Which of the choices is approximately 8? Certainly not A or B. Since \(\sqrt{2} \) nearly equals 1.4, Choices C, D, and E are approximately 4.2, 8.4, and 12.6, respectively. Clearly, the answer must be D.
Direct mathematical solution. Let s be a side of the square. Then since BCD is a 45-45-90 right triangle, \(s=\frac{3}{\sqrt{2}}\) \(= \frac{3\sqrt{2}}{2}\), and the perimeter of the square is 4s= \(\frac{3\sqrt{2}}{2}\) \(6 \sqrt{2}\).
Remember the goal of this book is to help you get credit for all the problems you know how to do, and, by using the TACTICS, to get credit for many that you don’t know how to do. Example 5 is typical. Many students would miss this question. You, however, can be sure that you will answer it correctly, even if you don’t remember how to solve it directly
