Problem 1
Answer: <u>Yes</u> a triangle can be formed with side lengths 5,5,3
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Explanation:
Take any two sides and add them up. If we get a sum larger than the third side, then a triangle is possible. This is the triangle inequality theorem.
5+5 = 10 is larger than 3
5+3 = 8 is larger than 5
This shows a triangle is possible. The triangle is isosceles because two sides are the same length.
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Problem 2
Answer: <u>Yes</u> a triangle can be formed with side lengths 8,8,8
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Explanation:
This triangle is equilateral because all sides are the same length.
Take any two sides, add them up, and you'll find the sum is larger than the third side.
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Problem 3
Answer: <u>No</u> a triangle cannot be formed with sides 7,8,15
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Explanation:
Yes it is true that
8+15 = 23 is larger than 7
7+15 = 22 is larger than 8
but
7+8 = 15 is not larger than 15
So this means a triangle is not possible.
Imagine you had 3 strips of paper that were 7 inches, 8 inches and 15 inches long. The 7 and 8 inch strips add to 15 inches, but those two smaller strips only form a straight line. We cannot pull them so a triangle forms. If we did, then the third side would be smaller than 15 inches. This is one way to get hands on to see why the triangle inequality theorem works.
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Problem 4
Answer: <u>Yes</u> a triangle is possible with side lengths 5,6,10
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Explanation:
Same idea as before. We can take any two sides, add them, and get a sum larger than the third side. A triangle is possible.
- 5+6 = 11 is larger than 10
- 6+10 = 16 is larger than 5
- 5+10 = 15 is larger than 6
