SOLUTION: An isoceles triangle has a side of 17 and a side of 35. What is the third side? Why?

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Question 811281: An isoceles triangle has a side of 17 and a side of 35. What is the third side? Why?
Found 3 solutions by josgarithmetic, richwmiller, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
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Represent two diagrams of isosceles triangles. One with a side 17 and two sides 35; and another triangle with one side 35 and two sides 17. A triangle inequality can be stated for each of these two situations, and you can find that one situation makes sense but the other situation does not.

17-17-35:
17%3C=17%2B35? yes.
35%3C=17%2B17? No.

17-35-35:
17%3C=35%2B35? yes.
35%3C=17%2B35? Yes.

One situation will clearly fail in the Triangle Inequality Test, while the other situation passes. The THREE side-lengths for this isosceles triangle are 17, 35, 35.

Answer by richwmiller(17219) About Me  (Show Source):
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The sum of any two sides must be greater than the third side
17+17=34 which is less than 35 so the third side must be 35.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

An isoceles triangle has a side of 17 and a side of 35. What is the third side? Why?

Third side MUST be greater than 18, but less than 52, but 17 is LESS than 18, so 17 CANNOT be one of its sides. Being an isosceles triangle, its third side MUST be highlight_green%2835%29.

You can do the check!!

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