Question 516383: 4. Which represents the lengths of the sides of an isosceles triangle?
3, 4, 5
6, 4, 5
12, 7, 7
15, 14, 13
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! By definition, an isosceles triangle is a triangle that has two sides that are equal in length.
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Notice that of the four triangles that are given, the only one that has two sides that are equal is the third triangle ... the one that has sides that are 12, 7, and 7.
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But you have to be careful in doing this. The one rule that you also have to meet is that the sum of the two shortest sides in a proposed triangle must be greater than the longest side. In this proposed triangle, the two shortest sides are 7 and 7. The sum of these two lengths is 14, and it meets the requirement of being greater than the longest side of 12.
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Why do you have to be careful? Because if you were given an answer of 12, 5, and 5 you might assume that this is an isosceles triangle. But if you tried to make a triangle having these dimensions, you would find that the two short sides will be too short in total length to form a triangle. (You might try to make such a triangle. Draw a 12 inch line on some paper. Then make two lines each 5 inches long. Connect the end of one of the 5 inch lines to one end of the 12 inch line. Then connect an end of the other 5 inch line to the other end of the 12 inch line. Then try to make the unconnected ends of the 5 inch lines join together to form a vertex of the triangle. It should become obvious to you that the two 5 inch lines will be too short to form a triangle with the 12 inch line.)
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Hope this helps you to understand the problem.
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