SOLUTION: What is the surface area of a rectangular prism with a length of 14 m, a height of 12 m, and a diagonal of 17.5 m

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Question 1113550: What is the surface area of a rectangular prism with a length of 14 m, a height of 12 m, and a diagonal of 17.5 m
Found 4 solutions by mananth, ikleyn, amalm06, greenestamps:
Answer by mananth(16946) About Me  (Show Source):
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The diagonal (d) of a prism is given by the formula
d%5E2=%28l%5E2%2Bb%5E2%2Bh%5E2%29
d%5E2-%28l%5E2%2Bh%5E2%29+=+width%5E2
w^2=33.75
w=5.81
formula for surface area
2(lw+lh+wh)
=
l=14, w=5.81 h =12
Plug them to get the answer




Answer by ikleyn(52790) About Me  (Show Source):
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.
What is the surface area of a rectangular prism with a length of 14 m, a height of 12 m, and a diagonal of 17.5 m
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As I understand the condition,  17.5 m is the  3D  diagonal,  or LONGEST diagonal.

But it immediately leads to the contradiction: 

    14%5E2 + 12%5E2 = 196 + 144 = 340.

    17.5%5E2 = 306.25.

As you see,  the sum of squares of two edges lengths is greater than the square of the longest  3D  diagonal.

Therefore,  I think that something is  WRONG  with the condition.

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If 17.5 m is not the 3D diagonal, then the problem MUST say directly and explicitly which EXACTLY diagonal is it.

The problem's formulation should not leave the gap for the student/(tutor) hypotheses or guessing - it is VERY BAD STYLE.


Answer by amalm06(224) About Me  (Show Source):
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Cannot be solved as written. The diagonal must be greater than the magnitude of the length squared plus the height squared.

Answer by greenestamps(13200) About Me  (Show Source):
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Tutor mananth overlooked the fact that her calculation of w^2 gave a negative answer, making the problem impossible.

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.

Tutor ikleyn was correct in noting that, and in saying that the problem, to be valid, must specify which diagonal has length 17.5.

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.

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.

However, as tutor ikleyn said, it is very bad form to submit a question where we have to guess what the real question is.