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the length, breadth and height of a shoe box is in the ratio 1:2:3. its total surface area is 792 sq. cm. find the dimensions of the shoe box.

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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

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