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Silvia is trying to box a gift for her cousin Hugo. The gift included

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Bunuel
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Silvia is trying to box a gift for her cousin Hugo. The gift included [#permalink] New post   29 Aug 2018, 03:55
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Silvia is trying to box a gift for her cousin Hugo. The gift included a rod that is 26 inches long and the box Silvia is using measures 8 inches long by 6 inches wide. If the rod fits exactly in the box when one end of the rod is placed in the lower right corner and the other end is placed in the upper left corner, how tall is the box?


A. 26
B. 25
C. 24
D. 23
E. 22
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C
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sumit411
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Re: Silvia is trying to box a gift for her cousin Hugo. The gift included [#permalink] New post   29 Aug 2018, 04:46
Bunuel wrote:
Silvia is trying to box a gift for her cousin Hugo. The gift included a rod that is 26 inches long and the box Silvia is using measures 8 inches long by 6 inches wide. If the rod fits exactly in the box when one end of the rod is placed in the lower right corner and the other end is placed in the upper left corner, how tall is the box?


A. 26
B. 25
C. 24
D. 23
E. 22
Imho
Answer is C
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Re: Silvia is trying to box a gift for her cousin Hugo. The gift included [#permalink] New post   29 Aug 2018, 07:35
Bunuel wrote:
Silvia is trying to box a gift for her cousin Hugo. The gift included a rod that is 26 inches long and the box Silvia is using measures 8 inches long by 6 inches wide. If the rod fits exactly in the box when one end of the rod is placed in the lower right corner and the other end is placed in the upper left corner, how tall is the box?


A. 26
B. 25
C. 24
D. 23
E. 22


\(d^2 = l^2 + b^2 + w^2\)

So, \(26^2 = 8^2 + b^2 + 6^2\)

Or, \(b^2 = 26^2 - 8^2 - 6^2\)

Or, \(b = \sqrt{676 - 64 - 36}\)

Or, \(b = 24\), Answer must be (C)
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Re: Silvia is trying to box a gift for her cousin Hugo. The gift included [#permalink] New post   03 Sep 2018, 19:03
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Bunuel wrote:
Silvia is trying to box a gift for her cousin Hugo. The gift included a rod that is 26 inches long and the box Silvia is using measures 8 inches long by 6 inches wide. If the rod fits exactly in the box when one end of the rod is placed in the lower right corner and the other end is placed in the upper left corner, how tall is the box?


A. 26
B. 25
C. 24
D. 23
E. 22


We can use the Pythagorean theorem for 3 dimensions to create the equation:

8^2 + 6^2 + h^2 = 26^2

64 + 36 + h^2 = 676

h^2 = 576

h = 24

Answer: C
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Re: Silvia is trying to box a gift for her cousin Hugo. The gift included [#permalink] New post   09 Oct 2019, 20:12
Expert Reply
Bunuel wrote:
Silvia is trying to box a gift for her cousin Hugo. The gift included a rod that is 26 inches long and the box Silvia is using measures 8 inches long by 6 inches wide. If the rod fits exactly in the box when one end of the rod is placed in the lower right corner and the other end is placed in the upper left corner, how tall is the box?


A. 26
B. 25
C. 24
D. 23
E. 22


We see that the length of the rod is the space diagonal of the box. If we let h = the height of the box, we can create the equation:

8^2 + 6^2 + h^2 = 26^2

64 + 36 + h^2 = 676

h^2 = 576

h = √576 = 24

Answer: C
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Re: Silvia is trying to box a gift for her cousin Hugo. The gift included [#permalink]
09 Oct 2019, 20:12
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