Problem on minimization

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A particle is moving in a rectangle ABCD with AB = 80 cm and AD = 60 cm. Given that the particle moves at 2 cm/s on the boundary of ABCD and moves at 1 cm/s inside the rectangle. Assume that the particle moves in straight lines. It starts from point A, moves towards the side DC, reaches a point P on DC and then to C. Let DP = x cm.

(a) Find the length of the path travelled by the particle from A to C in terms of x. (Ans: [√(x^2 + 3600) + (80 - x)] cm)
(b) Find the length of the path which takes the minimum time for the particle to travel from A to C. (Ans: 115 cm)
(c) What is the minimum time needed for the particle to travel from A to C? (Ans: 92.0 s)

Just using differentiation