Question 88042: Determine which set of numbers can be the measures of the sides of a triangle
Question 56 answers
2, 6, 3
3, 10, 13
4, 6, 1
5.1, 7, 2.3
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The way to do this problem is to identify the two smaller sides of the triangle. Add these two
smaller sides. Their sum must be greater than the largest side or a triangle cannot be
formed.
.
Let's work each of the four problems:
.
Given: sides of lengths 2, 6, and 3. The two smaller sides are 2 and 3. Add them together
and you get 5. This sum must be greater than the third side ... 6. Since 5 is not greater
than 6, a triangle cannot be formed.
.
Then given: 3, 10, 13. The two smaller sides are 3 and 10. Add them together to get 13.
Since this sum is not GREATER than the third side (which is also 13), a triangle cannot
be formed.
.
Given: 4, 6, 1. The two smaller sides are 1 and 4. Their sum is 5. A triangle cannot be
formed because 5 is not greater than the third side 6.
.
Finally, 5.1, 7, 2.3. The two smaller sides are 2.3 and 5.1. The sum of these two is
7.4. This time a triangle can be formed because this sum IS greater than the third side
which is 7.
.
One way to help you to visualize what is going on is to draw a horizontal line that is
equal in length to the long side. Then set a compass equal in length to the shortest side.
Put the point of this compass on the left end of the longest line and swing a circle with
the compass. Next set the compass to the length of the second shortest side. This time
put the point on the right end of the longest line and swing a second circle.
.
Then note that unless the two circles intersect above and below the longest side, a
triangle cannot be formed. If they do intersect above and below the longest line you can
connect the intersections with the ends of the longest lines and see the triangle(s)
that are formed.
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Hope this helps you to see the problem and how to solve it.
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