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Julius has a piece of string that is 24 inches long. He is stretching

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XavierAlexander
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Julius has a piece of string that is 24 inches long. He is stretching [#permalink] New post   29 Nov 2021, 14:54
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Julius has a piece of string that is 24 inches long. He is stretching the string around pegs on a pegboard to create different shapes.

Quantity A
Quantity B
The maximum area of a regular hexagon created by the string
The maximum area of a square created by the string




a). Quantity A is greater.


b). Quantity B is greater.


c). The two quantities are equal.


d). The relationship cannot be determined from the information given.
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elkk
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Re: Julius has a piece of string that is 24 inches long. He is stretching [#permalink] New post   30 Nov 2021, 01:06
Do we have perhaps an answer explanation to this problem? I'm not sure how to determine the max area of the hexagon. Thanks.
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XavierAlexander
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Julius has a piece of string that is 24 inches long. He is stretching [#permalink] New post   30 Nov 2021, 01:22
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Sorry, don't have the official explanation handy.
My thoughts: The word "strech" may create an ambiguity - as in how long a string is supposed to be streched to create the max. area? "Wrap" can be a better alternative. Solution --



Regular Hexagon ----> 6 eq. triangles (with side 'a')
perimeter = 6 * a
area = 6 * (√3/4 * a^2)
ref: https://www.math-only-math.com/perimete ... xagon.html



quantity A: 41.57
Perimeter = 6*a = 24
a = 4

Therefore, Area = 6 * (√3/4 * 4^2) = 24√3 = 41.57


quantity A: 36
Perimeter = 4*s = 24
s = 6

Therefore, Area = s^2 = 36


a). Quantity A is greater.

elkk wrote:
Do we have perhaps an answer explanation to this problem? I'm not sure how to determine the max area of the hexagon. Thanks.
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elkk
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Re: Julius has a piece of string that is 24 inches long. He is stretching [#permalink] New post   30 Nov 2021, 02:05
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OK Nice. I also just found the textbook answer. Apparently he divides the hexagon into two trapezoids and uses the trapezoid formula * 2. So one formula less to memorize 👍
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XavierAlexander
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Re: Julius has a piece of string that is 24 inches long. He is stretching [#permalink] New post   30 Nov 2021, 08:52
You're right.
In a similar way, 1st solution has the regular hexagon divided into 6 equilateral triangles. Thus, area of hexagon becomes --> 6 * (area of eq. triangle)

elkk wrote:
OK Nice. I also just found the textbook answer. Apparently he divides the hexagon into two trapezoids and uses the trapezoid formula * 2. So one formula less to memorize 👍
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Re: Julius has a piece of string that is 24 inches long. He is stretching [#permalink]
30 Nov 2021, 08:52
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