+0  
 
0
50
5
avatar+71 

tysm

 Jun 29, 2021

Best Answer 

 #1
avatar+234 
+3

Area of equilateral triangle: \(\frac{\sqrt{3}}{4}s^2\)

Area of regular hexagon: \(\frac{3\sqrt{3}}{2}s^2\)

 

If the perimeter of the triangle is 18, then one side is 6, therefore the area of it is,

\(\frac{\sqrt{3}}{4}\cdot36\)

\(area = 9\sqrt{3}\)

Because their areas are equal,

\(\frac{3\sqrt{3}}{2}s^2 = 9\sqrt{3}\)

Simplify,

\(3\sqrt{3}\cdot s^2 = 18\sqrt{3}\)

\(s^2 = 6\)

\(s = \sqrt{6}\)

There are 6 sides in a hexagon, so the perimeter is, \(\sqrt{6} \cdot 6 = 6\sqrt{6}\). 6 + 6 = 12, so that's the answer.

 

EDIT: I messed up my arithmetic

 Jun 29, 2021
edited by Awesomeguy  Jun 29, 2021
 #1
avatar+234 
+3
Best Answer

Area of equilateral triangle: \(\frac{\sqrt{3}}{4}s^2\)

Area of regular hexagon: \(\frac{3\sqrt{3}}{2}s^2\)

 

If the perimeter of the triangle is 18, then one side is 6, therefore the area of it is,

\(\frac{\sqrt{3}}{4}\cdot36\)

\(area = 9\sqrt{3}\)

Because their areas are equal,

\(\frac{3\sqrt{3}}{2}s^2 = 9\sqrt{3}\)

Simplify,

\(3\sqrt{3}\cdot s^2 = 18\sqrt{3}\)

\(s^2 = 6\)

\(s = \sqrt{6}\)

There are 6 sides in a hexagon, so the perimeter is, \(\sqrt{6} \cdot 6 = 6\sqrt{6}\). 6 + 6 = 12, so that's the answer.

 

EDIT: I messed up my arithmetic

Awesomeguy Jun 29, 2021
edited by Awesomeguy  Jun 29, 2021
 #2
avatar+120966 
+1

Nice solution Awesomeguy   !!!!

 

 

cool cool cool

CPhill  Jun 29, 2021
 #3
avatar+71 
0

CPhill, I don't think thats correct tho, the ans is 12.

justinwh333  Jun 29, 2021
 #4
avatar+234 
0

Yeah sorry i messed up my math

Awesomeguy  Jun 29, 2021
 #5
avatar+120966 
+1

No biggie....just a math mistake.....you  had  the correct approach   !!!!

 

 

cool cool cool

CPhill  Jun 29, 2021

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