The ratio of the length, width, and height of a cuboid is 4: 3 : 5 and the sum of the lengths of all its edges is 144 cm. Find the total surface area of the cuboid.

Explanation

Let the common ratio be x. Hence, the length, width, and height of the cuboid are 4x, 3x, and 5x respectively. According to the question, 4 × (4x + 3x + 5x) = 144 x = 3 Hence, the surface area of the cuboid = 2 (4x × 3x + 4x × 5x + 3x × 5x) = 2x2 (12 + 20 + 15) =2×32×47 =9×94 =846cm2