(1) AB = 9. We only know the length of one side. Not sufficient.
(2) BC = 4. We only know the length of one side. Not sufficient.
(1)+(2) If AB=AC=9 and BC=4 then the perimeter would be 9+9+4=22 but if AB=9 and AC=BC=4 then the perimeter would be 9+4+4=17. Not sufficient.
Answer to this question should be C, not E.What is the perimeter of isosceles triangle ABC?
(1) The length of side AB is 9. Clearly insufficient.
(2) The length of side BC is 4. Clearly insufficient.
(1)+(2) We know the lengths of the two sides of isosceles triangle ABC: AB=9 and BC=4, hence the length of AC is either 4 or 9. Relationship of the Sides of a Triangle: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Now, according to this, AC cannot equal to 4, because in this case the length of AB would be greater than the sum of the other two sides, AC and BC, (AB=9>AC+BC=4+4=8), hence AC=9 and P=9+9+4=22. Sufficient.
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For more check Triangles chapter of Math Book: math-triangles-87197.html
Hope it helps.
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