Help with applied optimization?

[heime]

SO this is the problem:
Find the rectangle of maximum area that can be inscribed in a right triangle with legs of length a=103 and b=104 if the sides of the rectangle x,y are parallel to the legs of the triangle.

I know that I'm supposed to find the derivative of the equation of the area, but I have no idea how to do that given that their are more than 1 unknown variables when I do that and I have no idea how to solve it afterwards. f someone could tell me how to do this step by step it would be greatly appreciated. :grin:

 

[mmm4444bot]

Did you draw a picture?

If you put the right-angle vertex at the origin, and draw the triangle in Quadrant I, then the lower-left corner of the inscribed rectangles will also be at the origin, and the upper-right corner will be on the hypotenuse.

Find the equation of the line going through the hypotenuse.

Define the height of the rectangles using the linear polynomial which defines that line.

Then x is the length.

The resulting area function (length times height) will have only one variable. (Consider the domain of this function.)

Questions? Work to show?

Please be sure to check out THIS PAGE, too. Cheers :cool: