Now, semi-perimeter of a triangle,
s=a+b+c2=35+54+612=1502=75cm
[∵ semi−perimeter, s=a+b+c2]
∵ Area of ΔABC=√s(s−a)(s−b)(s−c)
=√75(75−35)(75−54)(75−61)
=√75×40×21×14
=√25×3×4×2×5×7×3×7×2
=5×2×2×3×7√5=420√5cm2
Also Area of ΔABC=12×AB×Altitude
⇒ 12×35×CD=420√5
⇒ CD=420×2√535
∴ CD=24√5
Hence, the lenght of the longest altitude is 24√5 cm