Geometry finding length of a rectangular beam

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rachelmaddie

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The strongest rectangular beam is equal to the one whose length is 2.3 times the radius of the log.
Length = 2.3 x radius
Radius = diameter/2
Radius = 12/2
Radius = 6
Length = 2.3 x 6
The length of the strongest beam is 13.8 inches.
Is my work correct?218A4EC5-0D32-4326-9FEF-F0792CC69E41.jpeg
 
I think the problem is strange. Your work seems to be what they are telling you to do, but ...

The picture shows the cross-section of the log, which implies that the "length" would refer to the width or height as shown. It also says the beam is rectangular, not square, so one would expect the question to be about those dimensions. But since you can't cut anything bigger than 12 inches from a 12-inch log, that wouldn't make sense. It only makes sense if this "length", as I would expect from a beam, has nothing to do with the picture, but refers to the measurement along the length of the log, perpendicular to the picture. And the "beam" you end up with is only about 1 1/2 times as long as it is wide, nothing like anything I would call a beam.

I initially expected it to be saying the width is 2.3 times the height, which would be a much more interesting problem.
 
Dr.Peterson said:
I think the problem is strange. Your work seems to be what they are telling you to do, but ...

The picture shows the cross-section of the log, which implies that the "length" would refer to the width or height as shown. It also says the beam is rectangular, not square, so one would expect the question to be about those dimensions. But since you can't cut anything bigger than 12 inches from a 12-inch log, that wouldn't make sense. It only makes sense if this "length", as I would expect from a beam, has nothing to do with the picture, but refers to the measurement along the length of the log, perpendicular to the picture. And the "beam" you end up with is only about 1 1/2 times as long as it is wide, nothing like anything I would call a beam.

I initially expected it to be saying the width is 2.3 times the height, which would be a much more interesting problem.
Click to expand...
Would my work be correct in terms of the question being asked?
 
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