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17 Jun 2020, 03:56
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
29% (02:30) correct
71%
(02:51)
wrong
based on 98
sessions
History
Date
Time
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Not Attempted Yet
Squares A, B, C and D are placed as shown in the diagram above. Two smaller squares B and C have side length of 1. What is the area of blue triangle?
A. 2
B. 3
C. \(2\sqrt{2}\)
D. \(2\sqrt{3}\)
E. \(4\)
Are You Up For the Challenge: 700 Level Questions
Attachment:
2020-06-17_1424.png [ 44.8 KiB | Viewed 5102 times ]
23 Jun 2020, 09:02
Kudos
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Bunuel
Solution:
We are given the side lengths of squares B and C are both 1. Therefore, the side length of square A is 2. However, we are not given and we can’t determine the side length of square D. So let’s let the side length of square D be x. In addition, we will have a rectangle that encloses the 4 squares (see diagram below).
Attachment:
solution5.png [ 17.67 KiB | Viewed 4237 times ]
We see that if we subtract the sum of the areas of the two triangles above the shaded triangle and the trapezoid below it from the area of the rectangle that encloses the squares, then we have the area of the shaded triangle.
Area of the rectangle = 3(x + 2)
Area of the triangle above the shaded triangle to the right = ½(1)(1) = 1/2
Area of the triangle above the shaded triangle to the left = ½(3 - x)(x + 1) = ½(3 + 2x - x^2)
Area of the trapezoid below the shaded triangle = ½(x + 2)(x + 2) = ½(x^2 + 4x + 4)
Therefore, the area of the shaded triangle is:
Area = 3(x + 2) - [1/2 + ½(3 + 2x - x^2) + ½(x^2 + 4x + 4)]
Area = 3x + 6 - [1/2 + 3/2 + x - ½x^2 + ½x^2 + 2x + 2]
Area = 3x + 6 - [4 + 3x]
Area = 3x + 6 - 4 - 3x = 2
Answer: A
General Discussion
17 Jun 2020, 04:53
Kudos
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Bunuel
Please check the explanation as attched
Answer: Option A
Please check the video for the step-by-step solution.
Attachments
Screenshot 2020-06-17 at 5.23.18 PM.png [ 354 KiB | Viewed 4799 times ]
