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

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Joined: 02 Sep 2009
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29 Aug 2018, 03:55
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25% (medium)

Question Stats:

80% (02:00) correct 20% (02:05) wrong based on 54 sessions

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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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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
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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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03 Sep 2018, 19:03
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

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09 Oct 2019, 20:12
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

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# Scott Woodbury-Stewart

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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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