Fisrt let's formulate an equation based on what the word problem is giving us.
The lenght and width of a rectangle have a sum of 78= L + W=78
Then it's asking what dimensions give the maximum area, so you must know your Area equation=
Now plug this into your area equation
A= (78-W) (W)
Now a very interesting concept can be applied, we need to take the derivative of this equation, and must set A= 0.
*The (1) came to be because the derivative of a variable is 1. W^2 was changed to 2w because of the power rule of derrivatives, thsis sttes that we can bring out the power in front of the variable and subtract 1 from the exponent so we get 2w^1 which is 2W*
Now move things around and solve for W:
Now plug in value back into the L=78-W equation to solve for L
L= 78- 39
Hope this Helps :)