<p>The cube shown above has edges of length 2, and A and B are midpoints of two of the edges. What is the length of AB (not shown)?</p>
<p>Is the answer radical 6? If so, I can try and explain why. If not, I’m as lost as you.</p>
<p>Yeah, the answer is square root of 6, but I don’t understand why.</p>
<p>root 6.
Say the point/corner right below B as C and the point/corner on the right hand side of A as D, then ABC would be a right triangle if you can kinda picture a standing right triangle inside of the cube in your mind by looking at the picture. So you know the edges = 2, so we can figure out AD = 1, DC = 2, therefore AC would be root 5. You know BC = 1, and AC is root 5, use the same method, you can get AB = root 6.
Hopefully my explanation wasnt too bad I am actually not so good at teaching other ppl >.> Tell me if this makes sense to you!</p>
<p>You are being asked to find the “long diagonal” of a rectangular solid. For a long diagonal question you can use the Generalized Pythagorean Theorem:</p>
<p>d^2 = a^2 + b^2 + c^2</p>
<p>where a, b, and c are the length, width and height of the solid. </p>
<p>In this case a=1, b=2, and c=1.</p>
<p>So d^2 = 1^2 + 2^2 + 1^2 = 6, and thus d = sqrt(6).</p>
<p>Remark: You are not finding the long diagonal of the cube here. You are finding the long diagonal of a rectangular solid that is a portion of the cube.</p>
<p>Nrseries did just what I did. Couldn’t have said it better myself.</p>