Question 1040265
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A triangle has a perimeter of 24 inches. The medium side is 
3 more than the short side, and the longest side is 
5 times the length of the shortest side. Find the shortest side.
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<pre>
Let x be the shortest side length, in inches.
Then the medium side is (x + 3) inches,
while the longest side is 5x inches long.

The perimeter is the sum  x + (x+3) + 5x, so your equation is

x + (x+3) + 5x = 24.

Simplify and solve it

7x + 3 = 24  --->  7x = 24-3  --->  7x = 21  --->  x = {{{21/7}}} = 3.

Hence, the shortest side length is 3 in.
Then the medium side is x + 3 = 3 + 3 = 6 in
and the longst side is 5x = 5*3 = 15 in.

Now check if such a triangle does exist.
The sum of the lengths of the shortest and the medium sides is 3 + 6 in = 9 in.

It is less than the length 15 in of the longest side.

Hence, the triangle (3,6,15) actually doesn't exist.

It implies that the problem <U>HAS NO</U> solution.

<U>Answer</U>.  The problem <U>HAS NO</U> solution.  Such a triangle doesn't exist.
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