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 ifx cmis taken out, we are left with a square of dimensions(40-2x).

Then i found the area of the log's cross-section using:

$\displaystyle A= \pi (r)^2. This is = 1257cm^2$

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

$\displaystyle (-2x+40)(-2x+40) = 1257$

$\displaystyle 4x^2 - 160x +1600=1257$

$\displaystyle 4x^2 -160x +343= 0$

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.