The sides of a triangle are 35cm, 54cm and 61cm, respectively. The length of its longest altitude is

$b=$ 54cm

$c=$ 61cm

$s=\frac{a+b+c}{2}=\frac{35+54+61}{2}$ $=\frac{150}{2}=75$ cm

$A=\sqrt{s\times \left(s-a\right)\times \left(s-b\right)\times \left(s-c\right)}$

$=\sqrt{75\times \left(75-35\right)\times \left(75-54\right)\times \left(75-61\right)}$

$=\sqrt{75\times 40\times 21\times 14}$

$=\sqrt{25\times 3\times 2\times 5\times 7\times 3\times 7\times 2\times 4}$

$=5\times 3\times 2\times 7\times 2\sqrt{5}$

$=420\sqrt{5}$ cm

Longest altitude is

$420\sqrt{5}=\frac{1}{2}\times 35\times h$

$h=2\times 12\sqrt{5}$  cm

$h=24\sqrt{5}$  cm