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# The above cube has edges of length 5*2^(1/2). What is the perimeter of

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Joined: 02 Sep 2009
Posts: 50583
The above cube has edges of length 5*2^(1/2). What is the perimeter of  [#permalink]

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02 Sep 2018, 22:30
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Difficulty:

15% (low)

Question Stats:

80% (00:33) correct 20% (01:02) wrong based on 35 sessions

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The above cube has edges of length $$5\sqrt{2}$$. What is the perimeter of the triangle PQR?

A. 15

B. $$15\sqrt{2}$$

C. 30

D. 50

E. 100

Attachment:

image001.gif [ 705 Bytes | Viewed 557 times ]

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Re: The above cube has edges of length 5*2^(1/2). What is the perimeter of  [#permalink]

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02 Sep 2018, 23:43
Bunuel wrote:

The above cube has edges of length $$5\sqrt{2}$$. What is the perimeter of the triangle PQR?

A. 15

B. $$15\sqrt{2}$$

C. 30

D. 50

E. 100

Attachment:
image001.gif

Edge of cube = 5√2

Diagonal of any face of cube = Side√2 = 5√2*√2 = 10

PQ = QR = PR = Diagonal of faces of cube = 10 each

Perimeter of PQR = 10+10+10 = 30

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Re: The above cube has edges of length 5*2^(1/2). What is the perimeter of  [#permalink]

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02 Sep 2018, 23:49
Bunuel wrote:

The above cube has edges of length $$5\sqrt{2}$$. What is the perimeter of the triangle PQR?

A. 15

B. $$15\sqrt{2}$$

C. 30

D. 50

E. 100

Attachment:

1535961080985.jpg [ 54.49 KiB | Viewed 477 times ]
Attachment:

1535961080985.jpg [ 54.49 KiB | Viewed 477 times ]

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Re: The above cube has edges of length 5*2^(1/2). What is the perimeter of  [#permalink]

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11 Sep 2018, 16:15
Bunuel wrote:

The above cube has edges of length $$5\sqrt{2}$$. What is the perimeter of the triangle PQR?

A. 15

B. $$15\sqrt{2}$$

C. 30

D. 50

E. 100

Attachment:
image001.gif

We see that triangle PQR has three equal sides, each of which is a diagonal of a face of the cube. Since the cube has a side length of 5√2, the diagonal of a face is:

5√2 * √2 = 10, which is also a side of PQR, so the perimeter of PQR is 30.

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Re: The above cube has edges of length 5*2^(1/2). What is the perimeter of &nbs [#permalink] 11 Sep 2018, 16:15
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