Functions Corner Cut Off

A rectangle is made of blue paper, and measures 20 cm by 10 cm. A corner is cut off. The right angled triangle that is cut off has shorter sides (2p) cm and (p-1) cm. What values of p are valid? What is the length of the hypotenuse of the triangle that is cut off, in terms of p? What is the area remaining, in terms of p? Test out both formulae using the slider above.