the length of the hypotenuse of a 30-60-90 triangle is 18. what is the perimeter

The side opposite the 30 degree angle will be (1/2) as long as the hypoteneuse ... (9ft)

The side opposite the 60 degree angle will be (√3/2)  times as long as the hypoteneuse =

18* √3/2 = (9√3) ft

So the perimeter is (18 + 9 + 9√3) = (27 + 9√3) = 9(3 + √3) ft.