"Consider all the triangles formed by lines passing through the point (8/9,3) and both the x-axis and y-axis. Find the dimensions of the triangle with the shortest hypotenuse."
I tought I could manage this word problem but its hard to figure the equation stated by the given. I already drawed something in order to figure out what theorem to apply still had no progress. Sorry for the low quality picture wish someone could replace it
Try using the point-slope equation of a line and then find the $x$ and $y$ intercepts to get your height and width. The Pythagorean theorem will give you the length of the hypotenuse.
Take that hypotenuse length formula (dependent on the slope) and optimize by finding where the first derivative is equal to zero.