Question 891511
B - other side
C - hypotenuse
.
.
Use the Pythagorean theorem,
{{{3^2+B^2=C^2}}}
{{{9+B^2=C^2}}}
.
.
.
Perimeter,
{{{3+B+C=12}}}
{{{B+C=9}}}
{{{B=9-C}}}
.
.
Substitute,
{{{9+(9-C)^2=C^2}}}
{{{9+81-18C+C^2=C^2}}}
{{{18C=90}}}
{{{C=5}}}
Then,
{{{B=9-5}}}
{{{B=4}}}
The longest side is {{{5}}}