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08 Jun 2022, 05:45
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
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63% (01:46) correct
37%
(03:13)
wrong
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The above cube has edge of length 16. What is the area of the triangle PQR?
A. \(128\sqrt{3}\)
B. \(64\sqrt{3}\)
C. \(64\sqrt{2}\)
D. \(32\sqrt{3}\)
E. 48
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08 Jun 2022, 06:18
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Bunuel
Each of the sides of the triangle is the diagonal of one side of the square, so each side of the triangle is length \(16\sqrt{2}\).
In the attached drawing, we can see that we can find the height of the triangle by splitting it into two 30-60-90 triangles.
The area of the triangle is \(\frac{1}{2}bh\). \(\frac{1}{2}b=8\sqrt{2}\) and \(h=8\sqrt{2}\sqrt{3}\).
\(64*2*\sqrt{3}=128\sqrt{3}\)
Answer choice A.
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