Isosceles trio-formations!
Geometry
Level
3
How many different isosceles triangles can be drawn with sides that can be only 2 cm,3 cm,7cm or 11cm in length?Note that equilateral triangles are isosceles triangles.
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10
8
16
12
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The question is a direct application of the triangular inequality which says that the sum of any two sides of a trigon must exceed the sum of the third. So the pairs satisfying this are- ( 2 , 2 , 2 ) , ( 2 , 2 , 3 ) , ( 3 , 3 , 2 ) , ( 3 , 3 , 3 ) , ( 7 , 7 , 2 ) , ( 7 , 7 , 3 ) , ( 7 , 7 , 7 ) , ( 7 , 7 , 1 1 ) , ( 1 1 , 1 1 , 2 ) , ( 1 1 , 1 1 , 3 ) , ( 1 1 , 1 1 , 7 ) , ( 1 1 , 1 1 , 1 1 ) ...Thus total = 1 2