+0  
 
+1
51
2
avatar+2595 

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?

tertre  Apr 26, 2018

Best Answer 

 #1
avatar+92448 
+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

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

Melody  Apr 26, 2018
Sort: 

2+0 Answers

 #1
avatar+92448 
+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+2595 
+3

Thank you so much, Melody! smileysmiley

tertre  Apr 26, 2018

19 Online Users

avatar
avatar
New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy