Let the lengths of the three edges of the right rectangular prism be \(x\), \(y\), and \(z\) units. ∴ \(xy = a\) -----(i) \(yz = b\) -----(ii) \(zx = c\) -----(iii) Multiplying equations (i), (ii), and (iii), we get: \(x^2y^2z^2 = abc\) ⇒ \(xyz = \sqrt{abc}\) -----(iv) From equation (iv), dividing by (i), (ii), and (iii) respectively, we get: \(z = \cfrac{\sqrt{abc}}{a},\quad x = \cfrac{\sqrt{abc}}{b},\quad y = \cfrac{\sqrt{abc}}{c}\) ∴ The length of the space diagonal of the prism = \(\sqrt{x^2 + y^2 + z^2}\) units = \(\sqrt{\left(\cfrac{\sqrt{abc}}{b}\right)^2 + \left(\cfrac{\sqrt{abc}}{c}\right)^2 + \left(\cfrac{\sqrt{abc}}{a}\right)^2}\) units = \(\sqrt{\cfrac{abc}{b^2} + \cfrac{abc}{c^2} + \cfrac{abc}{a^2}}\) units = \(\sqrt{\cfrac{ac}{b} + \cfrac{ab}{c} + \cfrac{bc}{a}}\) units = \(\sqrt{\cfrac{a^2c^2 + a^2b^2 + b^2c^2}{abc}}\) units