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

Question

4706 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-15T19:02:26

Perimeter of triangle#=40.222ft#

#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#