The upper left-hand corner of a piece of paper 8 in. wide by 17 in. long is folded over to the right-hand edge. How would you fold it so as to minimize the length of the fold? In other words, how would you choose x to minimize y?
Where do x and y enter the picture ??
if you fold it it will create a right triangle. x is the base and y is the height.
Here is a solution to your problem, with sides 6 and 12
I suggest you print out the solution and change the constants to yours.
I suggest you are careful that your base of x, and height of y are consistent with the x and y in the solution
https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxminsol3directory/MaxMinSol3.html#SOLUTION 21
To minimize the length of the fold, you need to fold the paper in such a way that the folded portion is as short as possible.
Let's consider the given dimensions: the paper is 8 inches wide and 17 inches long. To find the value of x that minimizes the length of the fold (y), we can set up a right triangle using the folded portion as one side, with the folded side length as x, and the unfolded side length as (17 - x).
Now, to minimize the length of the folded portion (y), we can apply the Pythagorean theorem to the right triangle we formed:
(17 - x)^2 + 8^2 = y^2
Simplifying that equation, we get:
289 - 34x + x^2 + 64 = y^2
Combining like terms, we have:
x^2 - 34x + 353 = y^2
Now, we want to minimize the value of y, so let's find the minimum value of y by differentiating the equation with respect to x:
dy/dx = 2x - 34
Setting the derivative equal to zero to find the critical point:
2x - 34 = 0
2x = 34
x = 17
Therefore, x = 17 is the value that minimizes the length of the fold. This means that you should fold the paper halfway between the left and right edges to minimize the length of the fold.