Question 1113550
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Tutor mananth overlooked the fact that her calculation of w^2 gave a negative answer, making the problem impossible.<br>
Both she and tutor amalm06 assumed the diagonal is the space diagonal.  I believe it is standard convention that when talking about "the" diagonal of a rectangular prism it is the space diagonal.  But when the problem says the prism has "a" diagonal of 17.5m, it is open to interpretation.<br>
Tutor ikleyn was correct in noting that, and in saying that the problem, to be valid, must specify which diagonal has length 17.5.<br>
The dimensions of the prism are 12, 14, and x; a face with dimensions 12 by x and a face with dimensions 14 by x could both have diagonals of length 17.5.  Neither the space diagonal nor the diagonal on a face with dimensions 12 by 14 could have length 17.5.<br>
Given that the question asks for the surface area of the prism, I suspect the diagonal is supposed to be on the face with dimensions 14 by x.  That suspicion is based on recognizing that 14:17.5 = 4:5; so the third dimension of the prism is a rational number (10.5 -- making the ratio of the three dimensions 10.5:14:17.5 = 3:4:5), making it relatively easy to find the total surface area.<br>
However, as tutor ikleyn said, it is very bad form to submit a question where we have to guess what the real question is.