- Thread starter Nomadp
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Invoke Pythagoras and use:Can anyone please tell me the side length of a cube that has a longest diagnal of 11,400,576 feet??

L

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Do you know Pythagoras's Theorem?Thank you for your reply. I really don't know how to do that.

You do not knowThankyou for your reply. I really don't know how to do that.

If you do not know how to do it, here is a clue: the height, width, and depth of a

\(\displaystyle H^2 + W^2 + D^2 = WHAT?\)

Guess im not sure how to get that from the long diagonal inside a cubeYou do not knowhowto do this, or you do not understandwhyto do this?

If you do not know how to do it, here is a clue: the height, width, and depth of acubeare equal so

\(\displaystyle H^2 + W^2 + D^2 = WHAT?\)

You are not supposed to get that from the length of the longest diagonal.Guess im not sure how to get that from the long diagonal inside a cube

The point here is that a cube is symmetric. The length of the longest side equals the length of the shortest side; the length of the longest diagonal equals the length of the shortest diagonal.

\(\displaystyle x = y = z \implies x^2 + y^2 + z^2 = x^2 + x^2 + x^2 = WHAT?\)

1 chicken plus 1 chicken plus 1 chicken = how many chickens.

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I think you're saying that you don't know that \(\displaystyle L^2 + W^2 + H^2 = D^2\), where L, W, H are the length, width, height, and D is the diagonal through the solid.Guess im not sure how to get that from the long diagonal inside a cube

To obtain that fact, first think about the diagonal of one face. If X is the diagonal of an L x W face, then \(\displaystyle L^2 + W^2 = X^2\). But then this diagonal is perpendicular to a W x H face, so \(\displaystyle X^2 + H^2 = D^2\). Put this together, and you have \(\displaystyle L^2 + W^2 + H^2 = D^2\).

Pythagoras gave us a simple formula for finding the hypotenuse length of a triangle with a 90-degree angle in it, and this same formula is the basis of calculating the distance between two points. The cherry on top is that this formula works in

\(\displaystyle d = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 + (z_{2} - z_{1})^2 + ...}\)

This takes two points, \(\displaystyle (x, y, z, ...)_{1}\) and \(\displaystyle (x, y, z, ...)_{2}\), translates the first point to the origin, then calculates the magnitude of the resulting vector. If one corner of your cube is at the origin, what are the coordinates of the opposite corner?