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What is the length of an edge of a regular pyramid with the base of an

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Carcass
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What is the length of an edge of a regular pyramid with the base of an [#permalink] New post   22 Mar 2024, 05:01
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What is the length of an edge of a regular pyramid with the base of an equilateral triangle and a surface area of 96?

A. 11.31

B. 7.44

C. 5.66

D. 10.29

E. The answer cannot be determined from the information given.


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adewale223
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Re: What is the length of an edge of a regular pyramid with the base of an [#permalink] New post   06 Jul 2024, 16:07
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Let the length of an edge be y

Therefore

4 x root 3/4 x y^2


y^2 = 32 root 3

y = 7.44

Answer B

Adewale Fasipe, quant instructor from Lagos Nigeria.
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Re: What is the length of an edge of a regular pyramid with the base of an [#permalink] New post   19 Aug 2024, 03:30
adewale223 wrote:
Let the length of an edge be y

Therefore

4 x root 3/4 x y^2


y^2 = 32 root 3

y = 7.44

Answer B

Adewale Fasipe, quant instructor from Lagos Nigeria.



Could you please explain this in more detail. Where did 32 come from?
Thanks in advance
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What is the length of an edge of a regular pyramid with the base of an [#permalink] New post   19 Aug 2024, 07:51
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Each face of the pyramid has an area of \(\frac{96}{4}=24\)

Now we could calculate each side of each triangle the pyramid is formed of


Attachment:
pyramid.jpg
pyramid.jpg [ 10.77 KiB | Viewed 322 times ]



Using the ratio of the triangle 30:60:90

\(h=\frac{\sqrt{3}}{2}c, a=\frac{1}{2}c\)

Now use the area of the triangle

\(24=\frac{1}{2}*c*\frac{\sqrt{3}}{2}c\)


\(24*\dfrac{4}{\sqrt{3}}=c^2\)

\(c=7.44\)
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Re: What is the length of an edge of a regular pyramid with the base of an [#permalink] New post   19 Aug 2024, 11:48
Carcass wrote:
Each face of the pyramid has an area of \(\frac{96}{4}=24\)

Now we could calculate each side of each triangle the pyramid is formed of


Attachment:
pyramid.jpg



Using the ratio of the triangle 30:60:90

\(h=\frac{\sqrt{3}}{2}c, a=\frac{1}{2}c\)

Now use the area of the triangle

\(24=\frac{1}{2}*c*\frac{\sqrt{3}}{2}c\)

Thanks a bunch!


\(24*\dfrac{4}{\sqrt{3}}=c^2\)

\(c=7.44\)
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Re: What is the length of an edge of a regular pyramid with the base of an [#permalink]
19 Aug 2024, 11:48
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