In a triangle, product of all three sides is 960 and product of its inradius and circumradius is 16. Find the perimeter of triangle.

Solution : 

We know Formula for In-Radius 

r=Δ/s 

And for Circumradius

R=abc/4Δ  

So by using these two eq we have 

r*R = Δ/S*abc/4Δ = abc/4S 

Also r*R=16 given and abc= 960 given

So, 16=960/4*S 

S=15 

And we know S= a+b+c/2 

Therefore, S=P/2 and P = Perimeter =

 2*15=30 Ans .