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The given figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is10 units long.

Express the​ y-coordinate of P in terms of x.​ (Hint: Write an equation for the line​ AB.)
​(b) Express the area of the rectangle in terms of x.
​(c) What is the largest area the rectangle can​ have, and what are its​ dimensions?

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