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In the given problem, apply your knowledge in algebra and basic mathematics specially in solving volume of rectangular prism.

Given and It's Mathematical Equation

Rectangular packaging box is 73dm^3 more than the volume of a cube packaging box.

Vrectangular = 73 dm³ + Vcube

Vcube = s³

Vrectangular = lwh

→ lwh = s³ + 73 dm³

The length of the rectangular box is 1dm longer than twice the edge of the cube.

l = 2s + 1

Its height is 2dm shorter than the length of the edge of the cube.

h = s - 2

Width is 1dm longer than the cube’s edge.

w = s + 1

Solution

lwh = s³ + 73

(2s+1)(s-2)(s+1) = s³ + 73

(2s+1)(s²-s-2) = s³ + 73

2s³-2s²-4s+s²-s-2 = s³ + 73

2s³ - s² - 3s - 2 = s³ + 73

s³ - s² - 3s - 75 = 0

Solve for s using synthetic division.

s³ + s² - 2s - 74 = 0

s1 = 4.83245

s2 = -1.91622 + i * 3.44212

s3 = -1.91622 - i * 3.44212

Use the positive solution.

s = 4.83

w = s + 1 → w = 5.83

h = s - 2 → h = 2.83

l = 2s + 1 → l = 10.66

Answer

Dimension of a cube is 4.83 dm.

Dimension of a cube is 4.83 dm.Dimension of a rectangular box is 5.83 dm by 2.83 dm by 10.66 dm.

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