The strength S of a rectangular wooden beam is proportional to its width times the square of its depth. Find dimensions of the largest beam cut

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newstudent1234

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Q - The strength S of a rectangular wooden beam is proportional to its width times the square of its depth. Find the dimensions of the largest beam that can be cut be cut from a given size.

How do i solve this question, usually the diameter is given so I'm confused abt solving this?
 
newstudent1234 said:
Q - The strength S of a rectangular wooden beam is proportional to its width times the square of its depth. Find the dimensions of the largest beam that can be cut be cut from a given size.

How do i solve this question, usually the diameter is given so I'm confused abt solving this?
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Did you copy the question correctly? Perhaps there is a typo. The phrase "that can be cut be cut from a given size" makes no sense. Also, I expect it to ask about the strongest beam, not the largest beam!

But perhaps "a given size" means "a tree of a given diameter", and you are expected to call the diameter, say, D, and find the dimensions in terms of D. The ratio of width to depth will be independent of D.
 
They still say "largest" rather than "strongest", which is a mistake; but I think you need to do what I said and define a variable for the "given size", presumably the diameter of the log. And "shape" (as opposed to your "dimensions") implies all they want is the ratio, and your variable will not appear in the answer.

Exact words can make a difference! That's why we ask for them:

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