Hello, cutiepie!
A rectangle inscribed inside of an isosceles right triangle with hypotenuse 2.
What is the largest area a the rectangle can have, and what are its dimensions? I'll assume the diagram looks like this: Code:

1*
*  *
*  * P
*   +   o(x,y)
*    *
*   y *
*    *
  *    +   +   +    *  
1 x  x 1
Point is on the line: .[1]
The area of the rectangle is: . .[2]
Substitute [1] into [2]: .
Maximize: .
Substitute into [1]: .
Therefore, its dimensions are: .
. . and its maximum area is: .