1
Question
What is the perimeter of isosceles triangle ABC?
1. The length of side AB is 9
2. The length of side BC is 4
What is the perimeter of isosceles triangle ABC?
1. The length of side AB is 9
2. The length of side BC is 4
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Solution
The correct option is C C
The perimeter of a triangle is equal to the sum of the three sides.
(1) INSUFFICIENT: Knowing the length of one side of the triangle is not enough to find the sum of all three sides.
(2) INSUFFICIENT: Knowing the length of one side of the triangle is not enough to find the sum of all three sides.
Together, the two statements are SUFFICIENT. Triangle ABC is an isosceles triangle which means that there are theoretically 2 possible scenarios for the lengths of the three sides of the triangle:(1)AB = 9, BC = 4 and the thirdside, AC = 9 or (1)AB = 9,BC = 4 and the third side AC = 4.
These two scenarios lead to two different perimeters for triangle ABC, HOWEVER, upon careful observation we see that the second scenario is an IMPOSSIBILITY. A triangle with three sides of 4, 4, and 9 is not a triangle. Recall that any two sides of a triangle must sum up to be greater than the third side. 4 + 4 < 9 so these are not valid lengths for the side of a triangle.
Therefore the actual sides of the triangle must be AB = 9, BC = 4, and AC = 9. The perimeter is 22. The correct answer is C.
The perimeter of a triangle is equal to the sum of the three sides.
(1) INSUFFICIENT: Knowing the length of one side of the triangle is not enough to find the sum of all three sides.
(2) INSUFFICIENT: Knowing the length of one side of the triangle is not enough to find the sum of all three sides.
Together, the two statements are SUFFICIENT. Triangle ABC is an isosceles triangle which means that there are theoretically 2 possible scenarios for the lengths of the three sides of the triangle:(1)AB = 9, BC = 4 and the thirdside, AC = 9 or (1)AB = 9,BC = 4 and the third side AC = 4.
These two scenarios lead to two different perimeters for triangle ABC, HOWEVER, upon careful observation we see that the second scenario is an IMPOSSIBILITY. A triangle with three sides of 4, 4, and 9 is not a triangle. Recall that any two sides of a triangle must sum up to be greater than the third side. 4 + 4 < 9 so these are not valid lengths for the side of a triangle.
Therefore the actual sides of the triangle must be AB = 9, BC = 4, and AC = 9. The perimeter is 22.
The correct answer is C.
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