What is the ratio for the structure areas of the rectangular prisms shown below, given that they are similar and that the ratio of their edge lengths is 7: 3?

The ratio between their surface areas = 49/9

Step-by-step explanation:

* Lets revise the similarity of to prism

- If two prisms are similar, then there is a ratio between their

 corresponding dimensions

- There is a ratio between their volumes and surface area

- The the ratio between their corresponding dimensions is a/b,

  then the ratio between their volumes is (a/b)³ and the ratio between

 their surface area is (a/b)²

* Lets solve the problem

∵ The two rectangular prisms are similar

∵ The ratio between their corresponding sides is 7/3

∴ The ratio between their surface areas = (7/3)² = 49/9

* Lets check our answer

∵ The surface area of the rectangular prism is :

  S.A = Perimeter of base × its height + 2 × area of its base

- Find the surface area of the large prism

∵ The base has dimensions 14 units and 21 units

∵ Its height = 7 units

∵ The base is a rectangle

∵ Perimeter the rectangle = 2L + 2W

∵ Area the rectangle = L × W

∴ S.A = (2×14 + 2×21) × 7 + 2(14 × 21) = 1078 unit²

- Find the surface area of the small prism

∵ The base has dimensions 6 units and 9 units

∵ Its height = 3 units

∴ S.A = (2×6 + 2×9) × 3 + 2(6 × 9) = 198 unit²

- Lets find the ratio between them

∴ The ratio between surface areas of them = 1078/198 = 49/9

- It is the same with the answer above so we are right

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