Need help on a very simple geometry problem

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Homework Help Overview

The discussion revolves around a geometry problem involving a regular hexagon, where the relationship between the side length and the apothem is given. Participants are tasked with finding the lengths of both the side and the apothem based on the stated relationship.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the side length and the apothem, with attempts to derive a formula. Questions arise regarding the definitions and representations of variables used in the equations.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the precision of variable definitions, and there is an acknowledgment of potential alternative methods to approach the problem.

Contextual Notes

There are indications of confusion regarding variable representation, particularly the use of "a" to denote the apothem. Participants are also considering the implications of using different methods for solving the problem.

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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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