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# Herman is trying to box a gift for his cousin Edward. The gift include

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23 Aug 2018, 04:16
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15% (low)

Question Stats:

83% (01:57) correct 17% (01:48) wrong based on 21 sessions

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Herman is trying to box a gift for his cousin Edward. The gift included a rod that is 26 inches long and the box Herman 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. 12
B. 13
C. 24
D. 27
E. 104

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23 Aug 2018, 04:40
Bunuel wrote:
Herman is trying to box a gift for his cousin Edward. The gift included a rod that is 26 inches long and the box Herman 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. 12
B. 13
C. 24
D. 27
E. 104

The box in which Herman will fit the gift(which has a rod - 26 inches long) will be a cuboid.

We are given two dimensions of the cuboid - Length: 8 inches | Width: 6 inches. Since, the
maximum distance between any two points in a cuboid is the length of the diagonal, we can
find out the height of the cuboid using the formula of the diagonal in a cuboid

Formula used: Diagonal of cuboid = $$\sqrt{Length^2 + Width^2 + Height^2}$$

Substituting values, we get $$26 = \sqrt{8^2 + 6^2 + x^2}$$ (Here, x - height of cuboid)
Squaring on both sides, we will get $$26^2 = (\sqrt{64 + 36 + x^2})^2$$ -> $$x^2 = 576(676 - 100)$$

Therefore, the height of the box in which the rod fits exactly is $$\sqrt{576} = \sqrt{24^2}$$ = 24 (Option C)
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23 Aug 2018, 07:20
Bunuel wrote:
Herman is trying to box a gift for his cousin Edward. The gift included a rod that is 26 inches long and the box Herman 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. 12
B. 13
C. 24
D. 27
E. 104

Since the rod directly fits into the box then the diagonal of the box = 26

Now, $$26^2 = 8^2 + 6^2 + width^2$$

Or, $$676 = 64 + 36 + width^2$$

Or, $$Width = \sqrt{676 - 100}$$

Or, $$Width = 24$$, Answer must be (C)
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26 Aug 2018, 19:21
Bunuel wrote:
Herman is trying to box a gift for his cousin Edward. The gift included a rod that is 26 inches long and the box Herman 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. 12
B. 13
C. 24
D. 27
E. 104

We need to calculate the diagonal of the box.

We can use the formula:

L^2 + W^2 + H^2 = D^2

8^2 + 6^2 + H^2 = 26^2

64 + 36 + H^2 = 676

H^2 = 576

H = 24

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Re: Herman is trying to box a gift for his cousin Edward. The gift include   [#permalink] 26 Aug 2018, 19:21
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