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555-605 Level|   Geometry|      
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Bunuel
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The octahedron shown above is a solid figure whose eight equal faces 24 Oct 2019, 00:14
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B
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35% (medium)

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56% (01:06) correct 44% (01:10) wrong based on 63 sessions

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The octahedron shown above is a solid figure whose eight equal faces are equilateral triangles, each with perimeter 5. The sum of the lengths of all the edges of the octahedron is

(A) 13 1/3
(B) 20
(C) 26 2/3
(D) 40
(E) 60

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2017-12-08_1440_001.png
2017-12-08_1440_001.png [ 3.93 KiB | Viewed 1456 times ]
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B
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LevanKhukhunashvili
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The octahedron shown above is a solid figure whose eight equal faces 24 Oct 2019, 00:18
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The length of one edge is \(\frac{5}{3}\)
There are total of 12 edges

\(\frac{5}{3}*12=20\)

IMO
Ans: B
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The octahedron shown above is a solid figure whose eight equal faces 24 Oct 2019, 08:46
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Bunuel

The octahedron shown above is a solid figure whose eight equal faces are equilateral triangles, each with perimeter 5. The sum of the lengths of all the edges of the octahedron is

(A) 13 1/3
(B) 20
(C) 26 2/3
(D) 40
(E) 60

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Attachment:
2017-12-08_1440_001.png


from given info
3s=5
s=5/3
each side of ∆
so perimeter of octahedron ; 5/3*12 ; 20
IMO B
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The octahedron shown above is a solid figure whose eight equal faces 31 Oct 2019, 04:15
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Solution



Given
    • Octahedron shown above is a solid figure whose eight equal faces are equilateral triangles

To find
    • The sum of the lengths of all the edges of the octahedron

Approach and Working out
Let each edge is of a unit of the octahedron.
    • Hence, 3a = 5
      o a = 5/3
    • The octahedron has 12 edges. Hence, total length of all the edges = 5/3 *12 = 20
Thus, option B is the correct answer.

Correct Answer: Option B
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The octahedron shown above is a solid figure whose eight equal faces 31 Oct 2019, 04:20
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Alternate Method – Visualization


On visualization, you can see that there are:

    • 2 equilateral triangles + 2 more edges on the upper half of octahedron.
    • And, 4 more edges in lower half
      o So, if we combine the extra 2 edges of upper half into 4 edges of lower half, we will get 2 equilateral triangles in upper half and 2 in lower half.
      o Thus, 4 equilateral triangles.
    • Total length = Perimeter of 1 triangle * 4 = 5*4 = 20

Thus, option B is the correct answer.
Correct Answer: Option B
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