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

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

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Answer 1 · 2015-11-15T19:02:26

Perimeter of triangle $= 40.222 f t$ $=40.222ft$

Explanation:

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

where
$S S =$ $SS=$ Short Side,
$L S =$ $LS=$ Long Side,
$H =$ $H=$ Hypotenuse

The side-lengths can also be calculated with these relations
$S S = \frac{H}{2}$ $SS=H/2$ or $S S = \frac{1}{\sqrt{3}} L S$ $SS=1/sqrt3LS$
$L S = \frac{\sqrt{3}}{2} H$ $LS=sqrt3/2H$ or $L S = S S \sqrt{3}$ $LS=SSsqrt3$

Therefore, if $S S = 8.5 f t$ $SS=8.5ft$

$H = S S \times 2 = 8.5 \times 2 = 17 f t$ $H=SSxx2=8.5xx2=17ft$
and
$L S = 8.5 \sqrt{3} = 14.722 f t$ $LS=8.5sqrt3=14.722ft$

Hence,
Perimeter = Sum of all sides $= S S + L S + H = 40.222 f t$ $=SS+LS+H = 40.222ft$

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

1 Answer

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