Question

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

Answer 1

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`