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24 Jan 2022, 08:41
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:46) correct
39%
(02:23)
wrong
based on 75
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The figure shows a square surrounded by an equilateral triangle. If the edge x of the inscribed square is 12 inches long, then what is the perimeter of the equilateral triangle ?
A. \(36\) inches
B. \(36\sqrt{3}\) inches
C. \(36\sqrt{3}+24\) inches
D. \(24\sqrt{3}+36\) inches
E. \(72\) inches
Attachment:
2.JPG [ 24.29 KiB | Viewed 3144 times ]
Attachment:
Geo.png [ 8.28 KiB | Viewed 4011 times ]
24 Jan 2022, 17:15
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Bunuel
The figure shows a square surrounded by an equilateral triangle. If the edge x of the inscribed square is 12 inches long, then what is the perimeter of the equilateral triangle ?
A. \(36\) inches
B. \(36\sqrt{3}\) inches
C. \(36\sqrt{3}+24\) inches
D. \(24\sqrt{3}+36\) inches
E. \(72\) inches
Breaking Down the Graph:
The top shaded triangle is an equilateral triangle with a side of 12 inches. The other two smaller shaded triangles can be combined the build an equilateral triangle with a height of 12 inches, which will has a side length of \(12*\frac{2}{\sqrt{3}} = 8\sqrt{3}\)
Then the perimeter of the entire triangle is 12 + 12 from the top triangle, \(8\sqrt{3}*3\) from the left and right shaded triangles, and 12 from the bottom of the square. Thus \(36 + 24\sqrt{3}\) in total.
Answer: D
14 Feb 2022, 07:49
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2 concepts used:
1. Triangle above is equilateral with side = 12
2. 30-60-90 Triangle
Using both compute the length of side x 3 = perimeter
1. Triangle above is equilateral with side = 12
2. 30-60-90 Triangle
Using both compute the length of side x 3 = perimeter
