Question 234188: Given two sides with lengths 34 and 14, which of these lengths would NOT work for the third side of a triangle? 18, 34, 44, 22, 40
Found 3 solutions by stanbon, Edwin McCravy, MathTherapy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Given two sides with lengths 34 and 14, which of these lengths would NOT work for the third side of a triangle? 18, 34, 44, 22, 40
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Ans: 22
Why? because 14+22=34
Those three side lengths would give you a line segment 34 long.
They would not form a triangle.
Cheers,
Stan H.
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! Given two sides with lengths 34 and 14, which of these lengths would NOT work for the third side of a triangle? 18, 34, 44, 22, 40.
The sum of two sides of a triangle must always be greater than the third side.
So we'll make three checks on each choice.
Let's begin by trying 18.
Then the sides are 34, 14 and 18.
Add 34+14, that's 48, and that's greater than the third side, 18, so that
checks.
Add 34+18, that's 52, and that's greater than the third side, 14, so that
checks.
Add 14+18, that's 32, and that's NOT greater than the third side, 34,
so that DOES NOT check. So 18 will NOT work for the third side of
a triangle with sides 34 and 14.
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Let's try 34.
Then the sides are 34, 14 and 34.
Add 34+14, that's 48, and that's greater than the third side, 34, so that
checks.
Add 34+34, that's 68, and that's greater than the third side, 14, so that
checks.
Add 14+34, that's 48, and that's greater than the third side, 34, so that
checks.
So 34 DOES work for a third side for a triangle with sides 34 and 14.
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Let's try 44.
Then the sides are 34, 14 and 44.
Add 34+14, that's 48, and that's greater than the third side, 44, so that
checks.
Add 34+44, that's 78, and that's greater than the third side, 14, so that
checks.
Add 14+44, that's 58, and that's greater than the third side, 34, so that
checks.
So 44 DOES work for a third side for a triangle with sides 34 and 14.
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Let's try 22.
Then the sides are 34, 14 and 22.
Add 34+14, that's 48, and that's greater than the third side, 22, so that
checks.
Add 34+22, that's 56, and that's greater than the third side, 14, so that
checks.
Add 14+22, that's 36, and that's greater than the third side, 34, so that
checks.
So 22 DOES work for a third side for a triangle with sides 34 and 14.
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Let's try 40.
Then the sides are 34, 14 and 40.
Add 34+14, that's 48, and that's greater than the third side, 40, so that
checks.
Add 34+40, that's 74, and that's greater than the third side, 14, so that
checks.
Add 14+40, that's 54, and that's greater than the third side, 34, so that
checks.
So 40 DOES work for a third side for a triangle with sides 34 and 14.
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So the only choice that won't work for a third side of a triangle with
sides 34 and 14 is 18.
Why is that?
Suppose you had a triangle ABC drawn on the ground where AB is 34 feet,
AC is 14 feet, and BC is 18 feet. Since the shortest distance from A
to B is the straight line segment connecting them, namely AB, or 34 feet.
But if there were such a triangle it would be shorter to walk from A to C,
and then turn and walk from C to B, since AC is 14 feet and BC is 18 feet,
so that would be only 32 feet. So there can't be any such triangle.
Edwin
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Given two sides with lengths 34 and 14, which of these lengths would NOT work for the third side of a triangle? 18, 34, 44, 22, 40
The length that will not work is 18
This is because for any triangle, its 3rd side MUST be less than the sum of its other 2 sides, but greater than their difference.
Now, since the sum of 2 of its sides is 48 (34 + 14), and the difference of its 2 sides is 20 (34 - 14), it follows that 3rd side should be less than 48, but greater than 20. This means that 18 WILL NOT WORK!
In other words, 
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