a = 35, b = 54, c = 61

s = (a + b + c)/2

⇒ s = (35 + 54 + 61)/2 = 150/2 = 75.

Area(Δ) = √s(s-a)(s-b)(s-c)

⇒ Area(Δ) = √75(75-35)(75-54)(75-61)

⇒ Area(Δ) = √75×40×21×14

⇒ Area(Δ) = 420√5cm²

Area(Δ) = 1/2 × Base × Altitude

As the area of the triangle is fixed, for the longest altitude we need smallest base.

So, the length of base = 35cm

Area(Δ) = 1/2 × Base × Altitude

⇒ 420√5 = 1/2 × 35 × Altitude

⇒ 24√5 = Altitude.

Hence, the correct option is (C).