Let the length, breadth, and height of the rectangular box be \(a\) cm, \(b\) cm, and \(c\) cm respectively. So, \[ a + b + c = 24 \quad \text{—— (i)} \] and \[ \sqrt{a^2 + b^2 + c^2} = 15 \quad \text{—— (ii)} \] Now, \[ (a + b + c)^2 = 24^2 = 576 \Rightarrow a^2 + b^2 + c^2 + 2(ab + bc + ca) = 576 \] From (ii), \[ a^2 + b^2 + c^2 = 15^2 = 225 \Rightarrow 225 + 2(ab + bc + ca) = 576 \Rightarrow 2(ab + bc + ca) = 576 - 225 = 351 \] ∴ The total surface area of the rectangular box is 351 square centimeters