Need help on a very simple geometry problem

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A regular hexagon's side length is described as twice the square root of its apothem. The initial calculations suggested that the side length is represented as 2 times the square root of "a," where "a" is the apothem. However, confusion arose regarding the definition of "a," leading to incorrect conclusions about the relationship between the side and apothem. Suggestions were made to clarify the variables and consider alternative methods for solving the problem, including using numerical values. The discussion emphasizes the importance of precision in mathematical definitions and calculations.
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Homework Statement


a side of a regular hexagon is twice the square root of its apothem. Find the length of the apothem and the side

Homework Equations


a formula for special triangle
90 degree side is doubled the 30 degree side, and 60 degree side is root 3 times the 30 degree side

The Attempt at a Solution



after drawing the pictures and do the math, i got:
side: 2 times square root of a; a stands for apothem, an unknown value
apothem: square root of a times square root of three
 
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How about making a formula for the ratio length of side and apothem? Replace the side length of the hexagon from the info. Solve.
 
Modernization said:

Homework Statement


a side of a regular hexagon is twice the square root of its apothem. Find the length of the apothem and the side


Homework Equations


a formula for special triangle
90 degree side is doubled the 30 degree side, and 60 degree side is root 3 times the 30 degree side

The Attempt at a Solution



after drawing the pictures and do the math, i got:
side: 2 times square root of a; a stands for apothem, an unknown value
apothem: square root of a times square root of three

In your second line, you say that "a stands for apothem" (You mean that a stands for the length of the apothem- let's be precise!) but in the third line you say "apothem: square root of a times square root of three". Obviously a is not the length of the apothem in that line; what is a?
 
HallsofIvy said:
In your second line, you say that "a stands for apothem" (You mean that a stands for the length of the apothem- let's be precise!) but in the third line you say "apothem: square root of a times square root of three". Obviously a is not the length of the apothem in that line; what is a?
My answer was wrong.:confused: I'm guessing there's another method to solve this, like plugging in numbers... Instead of making X the unknown value, i used "a" .
 

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