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Each edge of the cube shown above has length n. What is the
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25 Nov 2020, 03:17
25 Nov 2020, 03:17
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Each edge of the cube shown above has length n. What is the perimeter, in terms of n, of quadrilateral \(ABDE\) ?
A. \(2n(1+\sqrt{2})\)
B. \(n \sqrt{2}\)
C. \(4n \sqrt{2}\)
D. \(4n\)
E. \(2n^2\)
Re: Each edge of the cube shown above has length n. What is the
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27 Nov 2020, 05:48
27 Nov 2020, 05:48
1
Carcass wrote:
Attachment:
GRE Each edge of the cube shown above has length n..png
Each edge of the cube shown above has length n. What is the perimeter, in terms of n, of quadrilateral \(ABDE\) ?
A. \(2n(1+\sqrt{2})\)
B. \(n \sqrt{2}\)
C. \(4n \sqrt{2}\)
D. \(4n\)
E. \(2n^2\)
Sides BD and AE are hypotenuse to right triangle CBD and FAE respectively.
Also BD = AE because it is a cube.
BD^2 = n^2 + n^2 --> 2n^2.
BD = 2n^2 under square root --> n√2 = AE as well.
Perimeter of quadrilateral ABDE in terms of n = n + n + n√2 + n√2.
= 2n + 2n√2 --> 2n(1+√2).
So, option A is the correct answer.
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Re: Each edge of the cube shown above has length n. What is the
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29 Nov 2020, 08:01
29 Nov 2020, 08:01
1
Here The perimeter of ABDE=2n+ 2*face diagonal
=2n+2n√2 =2n(1+√2)
A is the correct answer.
N:B: For a Cube there is two type of diagonal, one is face diagonal
another is main diagonal
Face diagonal =√(n^2+n^2)=n√2
Main diagonal =√(n^2+n^2+n^2)=n√3,as all sides=n
=2n+2n√2 =2n(1+√2)
A is the correct answer.
N:B: For a Cube there is two type of diagonal, one is face diagonal
another is main diagonal
Face diagonal =√(n^2+n^2)=n√2
Main diagonal =√(n^2+n^2+n^2)=n√3,as all sides=n
