Let x and y be the dimensions of the rectangle. If the perimeter is 40, we have
We can expression one variable in terms of the others as
Since the area is the product of the dimensions, we have
This is a parabola facing down, so it's vertex is the maximum:
So, the maximum is
And since we know that , we have as well.
This is actually a well known theorem: out of all the rectangles with given perimeter, the one with the greatest area is the square.
Do the parenthesis first because of using PEMDAS
y = 1/9x + 3 5/9
The slope between the two marked points is ...
... m = (change in y)/(change in x)
... = (4 -3)/(4 -(-5))
... m = 1/9
Then the point-slope equation for the line with slope m through point (h, k) can be written as ...
... y = m(x -h) +k
... y = 1/9(x -(-5)) +3 . . . . . m = 1/9, (h, k) = (-5, 3)
... y = 1/9x + 3 5/9 . . . . . . simplify
w/4 = 8
4/1 * w/4 = 8*4
Negative 6 and negative 9 would :)