Aright rectangular prism is enlarged by a scale factor of 7. what is the ratio of the surface area of the enlarged prism to the surface area of the original prism with a length of 5 inches, height of 4 inches, and a width of 3 inches?

First we look for the surface area of the original rectangular prism.
 We have then:
 A = 2 * (l * h) + 2 * (l * w) + 2 * (h * w)
 Where,
 l: length
 h: height
 w: width
 Substituting values:
 A = 2 * (5 * 4) + 2 * (5 * 3) + 2 * (4 * 3)
 A = 94 in ^ 2
 We are now looking for the enlarged prism area:
 A '= k ^ 2 * A
 Where,
 k: scale factor
 A: area of the original prism
 Substituting values we have:
 A '= (7) ^ 2 * (94)
 A '= 4606 in ^ 2
 The relation of areas is:
 A '/ A = 4606/96
 A '/ A = 49
 
 The ratio of the surface area of the enlarged prism to the surface area of the original prism is:
 A '/ A = 49

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