Final answer:
To find the dimensions of the shoe box, set up a system of equations using the given ratio and surface area. The dimensions are approximately Length: 4.22 cm, Breadth: 8.44 cm, Height: 12.67 cm.
Step-by-step explanation:
To find the dimensions of the shoe box, we need to set up a system of equations using the given ratio and surface area. Let's assume the length, breadth, and height of the shoe box are x, 2x, and 3x, respectively.
The total surface area of a shoe box is given by the formula:
2(length × breadth + breadth × height + height × length) = 792
Substituting the values in terms of x, we have:
2(x(2x) + (2x)(3x) + 3x(x)) = 792
Simplifying the equation:
4x² + 12x² + 3x² = 792/2
19x² = 396
x² = 396/19
x ≈ √(396/19) ≈ 4.22
Therefore, the dimensions of the shoe box are approximately:
Length: x ≈ 4.22 cm
Breadth: 2x ≈ 8.44 cm
Height: 3x ≈ 12.67 cm