Let the length, breadth, and height of the cuboid be \(a\) cm, \(b\) cm, and \(c\) cm respectively. Therefore, according to the question, \(\sqrt{a^2 + b^2 + c^2} = \sqrt{725}\) Or, \(a^2 + b^2 + c^2 = 725\) ——— (i) And, \(abc = 3000\) ——— (ii) And, \(2(ab + bc + ca) = 1300\) ——— (iii) Adding equations (i) and (iii), we get: \(a^2 + b^2 + c^2 + 2(ab + bc + ca) = 2025\) Or, \((a + b + c)^2 = 45^2\) Or, \(a + b + c = 45\) ——— (iv) Comparing equations (ii) and (iv), we get: \(a = 20\), \(b = 15\), and \(c = 10\) [\(a + b + c = 20 + 15 + 10 = 45\) and \(abc = 20 \times 15 \times 10 = 3000\)] Therefore, the length, breadth, and height of the cuboid are 20 cm, 15 cm, and 10 cm respectively.