Question

the net of a rectangular prism is shown below. the surface area of each face is labeled. which values represent the dimensions, in feet, of the rectangular prism? (note: diagram is not to scale) answer 3,9,36 27,36,108 3,4,12 3,9,12

Explanation:

Step1: Recall surface - area formulas

Let the dimensions of the rectangular prism be \(l\), \(w\), and \(h\). The surface - area of the faces are \(lw\), \(lh\), and \(wh\).

Step2: Check factor pairs

For an area of \(27\) square feet, factor pairs of \(27\) are \((1,27)\) and \((3,9)\). For an area of \(36\) square feet, factor pairs are \((1,36)\), \((2,18)\), \((3,12)\), \((4,9)\), \((6,6)\). For an area of \(108\) square feet, factor pairs are \((1,108)\), \((2,54)\), \((3,36)\), \((4,27)\), \((6,18)\), \((9,12)\).
If we assume the dimensions are \(3\), \(9\), and \(12\):

• \(3\times9 = 27\)
• \(3\times12=36\)
• \(9\times12 = 108\)

Answer:

3, 9, 12