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What is the sum of the lengths, in centimeters, of the two legs of a 30-60-90 right triangle, if the length of the hypotenuse is 2 sqrt 6 centimeters?

 

Thanks for all the help today!

 Feb 27, 2018
 #1
avatar+99580 
+1

The side opposite the 30°  is (1/2) of the hypotenuse  = √6 cm

 

The side opposite the 60° angle is  √3 times the side opposite the 30° angle  = √3 * √6

 

So...the perimeter is

 

√6 ( 1 + √3 + 2 )  =

 

√6 ( 3 + √3 )  cm

 

 

cool cool cool

 Feb 27, 2018
 #2
avatar+1432 
+1

You guys (and gals) are the best!  Thanks!

AnonymousConfusedGuy  Feb 27, 2018
 #3
avatar+1432 
+1

Actually, is this the only answer? It's showing up wrong...

AnonymousConfusedGuy  Feb 27, 2018
 #4
avatar+99580 
0

Try this, ACG.....

 

√6(3 + √3)  ≈  11.6 cm  

 

 

cool cool cool

CPhill  Feb 27, 2018
 #5
avatar+18049 
0

CPhill's answer is equal to  11.59....

ElectricPavlov  Feb 27, 2018
 #6
avatar+1432 
+1

Turns out it was a phrasing issue, it wanted sqrt6+3sqrt2 :/

AnonymousConfusedGuy  Feb 27, 2018

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