Question

Two corners of a triangle have angles of `( pi )/ 2` and `( pi ) / 4`. If one side of the triangle has a length of `1`, what is the longest possible perimeter of the triangle?

Answer 1

Longest possible perimeter is `3.4142`.

Explanation:

As two angles are `pi/2` and `pi/4`, third angle is `pi-pi/2-pi/4=pi/4`.

For longest perimeter side of length `1`, say `a`, has to be opposite smallest angle which is `pi/4` and then using sine formula other two sides will be

`1/(sin(pi/4))=b/sin(pi/2)=c/(sin(pi/4))`

Hence `b=(1xxsin(pi/2))/(sin(pi/4))=(1xx1)/(1/sqrt2)=sqrt2=1.4142`

and `c=1`

Hence longest possible perimeter is `1+1+1.4142=3.4142`.