If a rectangular prism's length, width, and height maintain a 6: 5: 4 proportion and its aggregate surface area equals 33300 cm2, state its respective dimensions in centimeters?
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Answer: D. 90, 75,60
Explanation
Expressing the rectangular prism dimensions as six x, five x, and four x incorporates the given proportional ratio. Substituting these algebraic dimensions into the aggregate surface area formula for a rectangular prism sets up an equation in terms of x squared. Solving the surface area equation for thirty three thousand three hundred square centimeters yields x equal to fifteen, giving dimensions ninety, seventy five, and sixty. The total surface area of a rectangular prism is the sum of the areas of all six of its rectangular faces. Proportional dimensions are represented algebraically by introducing a common scaling variable to each ratio term. Solving equations involving squared variables requires combining like terms and applying square root operations correctly.
Ninety, eighty five, and sixty features an incorrect middle dimension that violates the five parts proportion rule. Eighty five, seventy five, and sixty contains an incorrect first dimension that does not fit the six parts ratio. Ninety, seventy five, and seventy has an incorrect height dimension that fails the four parts ratio requirement.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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