Find Dimensions of a Log

Good day to All,

The question asked what are the dimensions of a square that can be cut from a cross-section of a tree log. The diameter of the log is given as 40cm. In my pic below it may not look like a square, but it is; sorry for the error produced in drawing it.

So, what i first deduced that if x cm is taken out, we are left with a square of dimensions (40-2x).
Then i found the area of the log's cross-section using:



Then I used length x width = Area to make a quadratic equation to solve for x:





Solving the Quad equ gives: x = 37.4 or 2.3 (37.4 exceeds)
The logical ans is 2.3, So> 40 - 2(2.3)= 36.4 cm
However, the ans is 33.9cm...
Thanks in advance.

If the log is perfectly cylindrical, then the largest square will have a diagonal that's the same length as the diameter of your circular cross section.

Since it's a square, the side lengths will be the same (x). Then we have by Pythagoras



So the dimensions of the largest square will be .

This exactly what I did in the beginning and used the diagonal of 40cm to make a right-angled triangle...but this gives x= 28.3cm not 33.9cm

Then the answer you have been given is wrong.

Hello, BobBali!

Quote:

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This exactly what I did in the beginning
and used the diagonal of 40cm to make a right-angled triangle.
But this gives x= 28.3cm, not 33.9cm

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Is there a typo?

Their answer works if the diameter is 48 cm.