Shortcut Trick For any cuboid, the sum of its dimensions can be found directly using the formula: Sum = √(Diagonal^(2) + Surface Area) ⇒ Sum = √(11^(2) + 240) ⇒ Sum = √(121 + 240) ⇒ Sum = √361 = 19 cm ∴ The correct answer is 19 cm. Alternate Method Given: Length of diagonal (d) = 11 cm Total Surface Area (S) = 240 cm^(2) Let the length, breadth, and height of the cuboid be l, b, and h respectively. • • • • • • • l h b d = 11 cm Area = 240 cm² Formula Used: Diagonal of a cuboid = √(l^(2) + b^(2) + h^(2)) Total Surface Area = 2(lb + bh + hl) Algebraic Identity: (l + b + h)^(2) = l^(2) + b^(2) + h^(2) + 2(lb + bh + hl) Calculations: ⇒ √(l^(2) + b^(2) + h^(2)) = 11 Squaring both sides: ⇒ l^(2) + b^(2) + h^(2) = 121 We are given the Surface Area: ⇒ 2(lb + bh + hl) = 240 Substituting these values into the standard algebraic identity: ⇒ (l + b + h)^(2) = 121 + 240 ⇒ (l + b + h)^(2) = 361 ⇒ l + b + h = √361 = 19 ∴ The correct answer is 19 cm. Related Concepts: Volume of a Cuboid The volume of a cuboid is the product of its length, breadth, and height: V = l × b × h. Sum of Length of All Edges Since a cuboid has exactly 12 edges (4 each of length, breadth, and height), the sum of their lengths is calculated as 4(l + b + h). Cube Properties For a cube with an edge side equal to 'a', the body diagonal is given by a√3, and the total surface area is 6a^(2).