Hello,
In an explanation to an OG question, Manhattan companion guide refers to a "deluxe pythagorean Theorem" as a means to determine the distance between two corners of a rectangular cube.
https://www.beatthegmat.com/deluxe-pytha ... 46196.html
In another Manhattan Problem, this time involving a square cube, this formula does not work.
https://www.beatthegmat.com/diagonals-of ... 82794.html
In which instances can this formula be applied?
Thanks!
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Deluxe Pythagorean Theorem
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The formula applies to both problems.HeyArnold wrote:Hello,
In an explanation to an OG question, Manhattan companion guide refers to a "deluxe pythagorean Theorem" as a means to determine the distance between two corners of a rectangular cube.
https://www.beatthegmat.com/deluxe-pytha ... 46196.html
In another Manhattan Problem, this time involving a square cube, this formula does not work.
https://www.beatthegmat.com/diagonals-of ... 82794.html
In which instances can this formula be applied?
Thanks!
The main diagonal of a rectangular solid is the longest line segment that can be drawn through the solid.
The determine the length of the main diagonal, use the Super-Pythagorean theorem.
If L=length, W=width, H=height, and D=diagonal, then:
L^2 + W^2 + H^2 = D^2
or
D = √(L^2 + W^2 + H^2).
In a cube, L=W=H.
If e = length of each edge, then:
e^2 + e^2 + e^2 = D^2
or
D = √(3e^2).
I used this last version of the formula in my solution to the problem about the cube:
https://www.beatthegmat.com/diagonals-of ... 82794.html
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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