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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?

 Apr 26, 2018

Best Answer 

 #1
avatar+99279 
+4

Draw an equilateral triangle of side length 2

now split it down the middle to form two congruent right angled triangles.

 

The angles on these 2 triangles are 90,60, and 30 degrees

the side lengths are  2,1 and sqrt3   (gained using Pythagoras's theorum)

 

The the hypotenuse of a similar triangle is 2root6 then that is a dilation of root6

 

2*sqrt6 = 2sqrt6

1*sqrt6 = sqrt6

sqrt3*sqrt6 = sqrt18 = 3sqrt2

 

Perimeter is

    \(2\sqrt6+\sqrt6+3\sqrt2\\ =3\sqrt6+3\sqrt2\;\;cm\)

.
 Apr 26, 2018
 #1
avatar+99279 
+4
Best Answer

Draw an equilateral triangle of side length 2

now split it down the middle to form two congruent right angled triangles.

 

The angles on these 2 triangles are 90,60, and 30 degrees

the side lengths are  2,1 and sqrt3   (gained using Pythagoras's theorum)

 

The the hypotenuse of a similar triangle is 2root6 then that is a dilation of root6

 

2*sqrt6 = 2sqrt6

1*sqrt6 = sqrt6

sqrt3*sqrt6 = sqrt18 = 3sqrt2

 

Perimeter is

    \(2\sqrt6+\sqrt6+3\sqrt2\\ =3\sqrt6+3\sqrt2\;\;cm\)

Melody Apr 26, 2018
 #2
avatar+3994 
+3

Thank you so much, Melody! smileysmiley

tertre  Apr 26, 2018

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