SOLUTION: The perimeter of a rectangle is 32m. Find the dimensions for which the diagonal is as short as possible
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Question 312445: The perimeter of a rectangle is 32m. Find the dimensions for which the diagonal is as short as possible
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1.
The diagonal is then,
2.
From the first equation,
Substituting into the second equation,
Now the distance squared is a function only of W.
Take the derivative wrt W and set it equal to zero to find the minimum.
Since D cannot be zero (since L and W are both not equal to zero), then must be zero when .
Then from above,
The minimum diagonal is formed by an 8m x 8m square.
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