The sides of a triangle are in the ratio of  $3:5:7$ If the perimeter of the triangle is 60 cm, then its area is

Side of a $\Delta$ are in the ratio $3:5:7$

I.e., $3x+5x+7x=60$

$15x=60$

$x=4$

$a=3x=3\times 4=12$ cm

$b=5x=5\times 4=20$ cm

$c=7\times 4=28$ cm

$s=\frac{a+b+c}{2}=\frac{12+20+28}{2}$

$=\frac{60}{2}=30$  cm

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

$=\sqrt{30\times \left(30-12\right)\times \left(30-20\right)\times \left(30-28\right)}$

$=\sqrt{30\times 18\times 10\times 2}$

$\sqrt{2\times 3\times 5\times 2\times 9\times 2\times 5\times 2}$

$=2\times 2\times 5\times 3\sqrt{3}=60\sqrt{3}{\text{cm}}^{\text{2}}$