1984 AHSME Problems/Problem 25
Problem
The total area of all the faces of a rectangular solid is , and the total length of all its edges is . Then the length in cm of any one of its interior diagonals is
Solution
Let the edge lengths be , and . Therefore, the total area of all its faces is . Therefore, and . Also, the total lengths of all of its edges is , so , and . Therefore, we have:
and
.
The length of the interior diagonal is , so if we can find , we can find the diagonal. We square the second equation above to introduce an :
.
However, we already know that , so .
See Also
1984 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Problem 26 | |
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