chetan2u wrote:
PQR is an isosceles triangle. What is its perimeter?
1) Side PQ = 6
2) Side PR = 2
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and BTarget question: What is the perimeter of isosceles triangle PQR? Given: PQR is an isosceles triangle Statement 1: Side PQ = 6 There are many isosceles triangles that satisfy statement 1. Here are two:
Case a: PQ = 6, PR = 6 and RQ = 5. Note that this is an isosceles triangle AND it meets the above
rule. In this case,
the perimeter = 6 + 6 + 5 = 17Case b: Case a: PQ = 6, PR = 6 and RQ = 4. Note that this is an isosceles triangle AND it meets the above
rule. In this case,
the perimeter = 6 + 6 + 4 = 16Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Side PR = 2 Applying the same logic we used for statement 1, we can see that statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that one side has length 6
Statement 2 tells us that one side has length 2
Since PQR is an
isosceles triangle, the third side (RQ) must have length 6 or 2 (so that we have two sides of equal length).
If side RQ has length 6, then the sides have length 6, 6, and 2. These three lengths satisfy the above
rule, in which case,
the perimeter = 6 + 6 + 2 = 14 If side RQ has length 2, then the sides have length 6, 2, and 2. These three lengths DO NOT satisfy the above
rule. If we make the side with length 6 the third side, and apply the
rule, we get 2 - 2 < 6 < 2 + 2. When we simplify this, we get 0 < 6 < 4
So, the three lengths CANNOT be 6, 2 and 2.
So,
the perimeter MUST be 14Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer:
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