Question

each of the cubes in the figure has an edge length of 1. find the length of segment mn. (1)mn can be seen as a space diagonal of a rectangular prism with dimensions

Explanation:

Step1: Analyze the horizontal, vertical and depth - wise lengths

Count the number of unit cubes along the three mutually perpendicular directions (length, width, height) from \(N\) to \(M\).
Along the horizontal direction (let's say \(x\) - direction), the number of unit cubes is \(2\).
Along the vertical direction (let's say \(y\) - direction), the number of unit cubes is \(3\).
Along the depth - wise direction (let's say \(z\) - direction), the number of unit cubes is \(2\).

Step2: Use the space - diagonal formula for a rectangular prism

The formula for the space - diagonal \(d\) of a rectangular prism with length \(l\), width \(w\), and height \(h\) is \(d=\sqrt{l^{2}+w^{2}+h^{2}}\). Here, if \(l = 2\), \(w=2\), \(h = 3\)

Answer:

\(2\times2\times3\)