Why can C not be the total surface area of 2 faces? is it because we were able to find surface area bigger than 128 ( if L=10, W=8 , Area =80 *2 = 160)

Trying to understand why we select E over C.

I think you have not considered all the possible cases for this question.

L = 6, B = 8, H = 10

- L*B = 48
- B*H = 80
- L*H = 60

The sum of any two surfaces can be calculated for 6 cases. 3 cases arise when we combine 2 different faces and an additional 3 cases arise when the two faces considered are same.

Case 1:

- 48 + 80 = 128 (C is possible therefore not the answer)
- 48 + 60 = 108
- 80 + 60 = 140

Case 2:

- 48 + 48 = 96 (A is possible therefore not the answer)
- 80 + 80 = 160 (D is possible therefore not the answer)
- 60 + 60 = 120 (B is possible therefore not the answer)

Hence, we are only left with E option which is not achievable

Alternatively, you could have found the maximum total area for 2 faces which will be 160. Hence, 180 cannot occur. However, this is specific to this problem and may not work if the options or question type changes.

Ahh ok! We can take any 2 faces, not just the same 2 faces. I got 120,160 and 96 based (Case 2) but didn’t realize we need to test faces that are not the same as well. Makes sense now! Thanks so much