Hi can someone please help?
I need to find the rectangle of maximum area that can be inscribed in a right triangle with legs of length $a=53$ and $b=54$ if the sides of the rectangle $x,y$ are parallel to the legs of the triangle.
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Maybee this image from mathalino.com will make you realize how to come up with the formula for the area of the rectangle in terms of $x$:
Think similar triangles.
Once you have the formula $f(x)=A$ find its maximum on the interval $[0,53]$ or $[0,54]$ depending on which leg you put on your horizontal $x$ axis. Consider $f'(x)=0$ or the endpoints of your interval.