If the shortest leg of the 30-60-90 triangle is 8.5 ft, then what is the perimeter?

1 Answer
Nov 15, 2015

Perimeter of triangle=40.222ft

Explanation:

30^o-60^o-90^o is a special kind of right-triangle in which sides exist in ratio SS:LS:H = 1:sqrt(3):2

where
SS=Short Side,
LS=Long Side,
H=Hypotenuse

The side-lengths can also be calculated with these relations
SS=H/2 or SS=1/sqrt3LS
LS=sqrt3/2H or LS=SSsqrt3

Therefore, if SS=8.5ft

H=SSxx2=8.5xx2=17ft
and
LS=8.5sqrt3=14.722ft

Hence,
Perimeter = Sum of all sides=SS+LS+H = 40.222ft