There are several approaches. The most favourable one (in my opinion) is this one:
1. Asking a question
2. Doing a research (how to answer this question)
3. Creating a hypothesis (NOT a thesis!)
4. Experimenting (to prove the hypothesis)
5. Analysing results from the experiment
6. Writing a thesis
Answer:
475 m , 950 m
Explanation:
Let l be the length of the side perpendicular to the barn.
1900-2l = length of the side parallel to the barn
Area A= l( 1900-2l)
A= 1900l-2l^2
now, the maximum value of l ( the equation being quadratic)
l_max= -b/2a
a= 2
b=1900
l_max= -1900/4= 475 m
then 1900-2l= 1900-2×(475) = 950 m
So, the dimensions that maximize area are
950 and 475
Now. A_max = -2( l_max)^2+1900×l_max
A_max= -2(475)^2+1900×475
A_max= 451250 m^2
or, 475×950 = 451250 m^2
A developing story hope it helped
