The length, the breadth, and the height of a closed cardboard box are in the ratio of 5 : 3 : 7, respectively. Find the length of this box, if its total surface area is 1278 cm².

15 cm

We know that,

Total Surface area of cardboard box = 2(lb + bh +hl)

We have,

length, width and height ratio = 5 : 3 : 7

Total Surface area = 1278 cm²

Let, length = 5x

 width = 3x

height = 7x

Total Surface area of cardboard box =  2(5x × 3x + 3x × 7x + 7x × 5x) = 1278 cm²

= 2(15x² + 21x² + 35x²) = 1278 cm²

= (71x²) = 639

= x² = 9

= x = 3

Length of the box = 5 × 3 = 15cm