# diagonal formula of rectangular prism

#### BioTic

I know for the diagonal of the longest line it's square root ( l^2+w^2+h^2). Is there a formula to find the shortest line? I need to know how to solve this problem without unfolding.
Thanks

#### WheatLom

2+ Year Member
Ill answer this, haha. Im 1 hour away from the test.

So the longest line. I usually just find the hypotenuse of the base (90)^1/2 and then I know the height is 5 so there you got the base and height.

The smallest diagonal will be along the shortest sides. so the 3 by 5 side will have the shortest. and thats just straight pythagorean theorem. It is fool proof, no formulas.

#### BioTic

I found the diagonal of the longest line to be square root of 115, so how is the diagonal of the shortest line square root of 145?
Good luck

Anyone?

#### lxx

2+ Year Member
Hello,

For this problem, I don't think you can do it without any unfolding, just minimize the amount you have to do. I say this because you have to visualize the unfolding process a little bit to know how the triangle's dimensions should more or less come out to be. Also, there isn't really a formula that one can use because the distances you use as your triangle legs will vary depending on the specific position of the points. However, for this specific problem, the formula would be sqrt[(w + h)^2 + l^2].

You are correct in saying that the longest diagonal line is sqrt(115); the answer to the question does not suggest anything to the contrary. The aforementioned value is the distance between points A and B when you go through the rectangular prism. You are trying to find the shortest distance going along the surface of the object

Choices D and E are the distances between the two points when one calculates the hypotenuse of one of the faces then goes along the edge.

Hope this helped 