+0  
 
+1
108
1
avatar

Two congruent squares are placed in an equilateral triangle of side length 8.  Find the side length of each square.

 

 Dec 29, 2019

Best Answer 

 #1
avatar+22096 
+1

x = square side length

 

Triangle in bottom right has base length of     (8 - 2x)/2   

 

Tan 60 = opp/adj  = x / (8-2x)/2   = 2x/(8-2x)     tan 60 = sqrt 3

 

sqrt 3 = 2x/(8-2x)

8 sqrt 3 - 2x sqrt 3 = 2x

8 sqrt 3 = 2x + 2x sqrt 3

8 sqrt 3 = x (2+ 2 sqrt 3)

 

( 8 sqrt 3) / (2+2 sqrt 3) = x

 rationalize the denominator to get

 

x = 6- 2 sqrt 3

 Dec 29, 2019
 #1
avatar+22096 
+1
Best Answer

x = square side length

 

Triangle in bottom right has base length of     (8 - 2x)/2   

 

Tan 60 = opp/adj  = x / (8-2x)/2   = 2x/(8-2x)     tan 60 = sqrt 3

 

sqrt 3 = 2x/(8-2x)

8 sqrt 3 - 2x sqrt 3 = 2x

8 sqrt 3 = 2x + 2x sqrt 3

8 sqrt 3 = x (2+ 2 sqrt 3)

 

( 8 sqrt 3) / (2+2 sqrt 3) = x

 rationalize the denominator to get

 

x = 6- 2 sqrt 3

ElectricPavlov Dec 29, 2019

37 Online Users

avatar
avatar