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A net of a rectangular prism is shown below. The surface area of each face is labeled.      40 m212 m2 30 m2 12 m230 m2      40 m2Which values represent the dimensions, in meters, of the rectangular prism?

Question

A net of a rectangular prism is shown below. The surface area of each face is labeled.      40 m212 m2 30 m2 12 m230 m2      40 m2Which values represent the dimensions, in meters, of the rectangular prism?

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Solution

The dimensions of the rectangular prism can be determined by looking at the surface area of each face.

  1. The two faces with a surface area of 40 m2 each must be the length and the width of the prism. To find the dimensions, we need to find two numbers that multiply to 40. These could be 4 m and 10 m, or 5 m and 8 m, or 2 m and 20 m, etc.

  2. The two faces with a surface area of 30 m2 each must be the length and the height of the prism. To find the dimensions, we need to find two numbers that multiply to 30. These could be 3 m and 10 m, or 5 m and 6 m, or 2 m and 15 m, etc.

  3. The two faces with a surface area of 12 m2 each must be the width and the height of the prism. To find the dimensions, we need to find two numbers that multiply to 12. These could be 3 m and 4 m, or 2 m and 6 m, or 1 m and 12 m, etc.

However, since the same dimensions must be used for all faces, we need to find a common set of dimensions. The only set of dimensions that fits all three pairs of faces is 4 m (height), 6 m (width), and 10 m (length).

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