Math Problem Statement
Solution
The problem given is about a rectangular prism (box) with the ratio of its length, width, and height being . The area of the base (length width) of the box is given as . We need to determine the dimensions of the box.
Let's denote the length, width, and height of the box as , , and respectively, where is a scaling factor.
Given the area of the base:
We can solve for and subsequently for , then calculate the dimensions of the box:
With :
- Length = cm
- Width = cm
- Height = cm
Thus, the dimensions of the box are:
- Length: 15 cm
- Width: 9 cm
- Height: 6 cm
Would you like more details on this or have any other questions? Here are some related questions you might consider:
- How would you determine the volume of this box?
- What happens if the ratio of dimensions is changed?
- How would you solve this problem if only the volume and one dimension were given?
- Can you derive a general formula for the dimensions based on the area of the base and the ratio?
- What are the implications of using different units, such as meters instead of centimeters?
Tip: When given a problem involving ratios, it's often helpful to introduce a scaling factor, represented by , to easily manipulate and solve equations that involve proportions.
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Math Problem Analysis
Mathematical Concepts
Ratios
Geometry
Algebra
Formulas
Length × Width = Area of the base
Scaling factor k: 5k, 3k, 2k for length, width, and height
Theorems
Area of a rectangle
Suitable Grade Level
Grades 7-9
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