we let shorter leg be a. By special property of 30-60-90 triangle, hypotenuse=2a, then longer leg=sqrt3*a. Thus area is sqrt3 / 2 * a^2. Equal to altitude times base over two.
Hence altitude times base is a^2 * sqrt 3. base is 2a, so altitude is a * sqrt3 /2=5 --> a=10/(sqrt3). perimeter is 10/(sqrt3)+20/(sqrt3)+10=10sqrt3+10.
