Re: Find Dimensions of a Log

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

$\displaystyle \displaystyle \begin{align*} x^2 + x^2 &= 40^2 \\ 2x^2 &= 1600 \\ x^2 &= 800 \\ x &= \sqrt{800} \\ x &= 20\sqrt{2} \end{align*}$

So the dimensions of the largest square will be $\displaystyle \displaystyle \begin{align*} 20\sqrt{2} \times 20\sqrt{2} \end{align*}$.

Re: Find Dimensions of a Log

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

Re: Find Dimensions of a Log

Then the answer you have been given is wrong.

Re: Find Dimensions of a Log

Hello, BobBali!

Quote:

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

Is there a typo?

Their answer works if the diameter is 48 cm.