Is area of triangle ABC greater than area of triangle DEF ?
1. The value of area of ABC is less than that of perimeter of DEF.
2. Angles of ABC = Angles of DEF
Test an EASY CASE.
Let ∆ABC and ∆DEF each be a 45-45-90 triangle.
The sides of a 45-45-90 triangle are in the following ratio:
1:1:√2.
Statement 1: The value of the area of ∆ABC is less than that of the perimeter of ∆DEF
Case 1: ∆ABC = 1:1:√2 (area = 1/2) and ∆DEF = 1:1:√2 (perimeter ≈ 3.4)
Here, the two areas are equal, so the answer to the question stem is NO.
Case 2: ∆ABC = 2:2:2√2 (area = 2) and ∆DEF = 1:1:√2 (perimeter ≈ 3.4)
Here, ∆ABC has a greater area, so the answer to the question stem is YES.
INSUFFICIENT.
Cases 1 and 2 satisfy BOTH STATEMENTS.
Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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