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√5 cm2
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).
