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

Algebra ->  Points-lines-and-rays -> 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      Log On


   

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) About Me  (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) About Me  (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:

%28x%29%2B%28x%2B5%29%3E4x
5%3E2x
x%3C2.5

The perimeter is p+=+x%2Bx%2B5%2B4x+=+6x%2B5; since x%3C2.5, p%3C6%282.5%29%2B5=20.

A perimeter of 23 inches is not possible.

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

There is NO triangle satisfying the given desription.

The posed problem HAS NO solution.