SOLUTION: A triangle has a perimeter of 23 inches. The medium side is 5 more than the short side, and the longest side is 4 times the length of the shortest side. Find the shortest sid

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Question 1163816: A triangle has a perimeter of 23
inches. The medium side is 5
more than the short side, and the longest side is 4
times the length of the shortest side. Find the shortest side.
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
short           x
medium          x+5
long            4x
SUM              23


Recheck against Triangle Inequality Theorem.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Faulty problem description.

If the longest side is 4 times as long as the short side, and the medium side is only 5 inches longer than the short side, you can't have a perimeter of 23 inches.

The sum of the lengths of the two shorter sides has to be greater than the length of the longest side:





The perimeter is ; since , .

A perimeter of 23 inches is not possible.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

There is NO triangle satisfying the given desription.

The posed problem HAS NO solution.



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