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Problem Solving Question - Geometry

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by Smriti Shashikumar » Sun Mar 10, 2013 1:14 am
A straight inflexible metal rod with negligible diameter has to be imported through shipping, which should be packed in a rectangular box with dimensions 6 meters by 8 meters by 24 meters respectively. What is the maximum length of the rod that can be fit in the box?

A. 24
B. 25.2
C. 26
D. 34
E. 38

Thanks for the help!
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by Anju@Gurome » Sun Mar 10, 2013 1:24 am
Smriti Shashikumar wrote:A straight inflexible metal rod with negligible diameter has to be imported through shipping, which should be packed in a rectangular box with dimensions 6 meters by 8 meters by 24 meters respectively. What is the maximum length of the rod that can be fit in the box?
Maximum length of the rod = Length of the principal diagonal of the box = √(6² + 8² + 24²) = √(36 + 64 + 576) = √676 = 26

The correct answer is C.
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by GMATGuruNY » Sun Mar 10, 2013 3:21 am
Smriti Shashikumar wrote:A straight inflexible metal rod with negligible diameter has to be imported through shipping, which should be packed in a rectangular box with dimensions 6 meters by 8 meters by 24 meters respectively. What is the maximum length of the rod that can be fit in the box?

A. 24
B. 25.2
C. 26
D. 34
E. 38

Thanks for the help!
The longest line that can be drawn inside a rectangular solid is called the MAIN DIAGONAL.
Use the SUPER-PYTHAGOREAN THEOREM.
If d = the length of the main diagonal, then:
d² = l² + w² + h².

In the problem above:
d² = 6² + 8² + 24²

d² = 2²3² + 2²4² + 2²12²

d² = 4(9 + 16 + 144)

d² = 4*169

d = 2*13

d = 26.

The correct answer is C.
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