We're asked to find the area of a rectangle, which means we need to know its exact length and width.
Fact 1: The diagonal is 5.
You are correct that the Pythagorean Theorem is appropriate here:
L^2 + W^2 = 5^2
HOWEVER, we were NOT told that the two dimensions have to be integers.
The two dimensions COULD be 3 and 4, in which case the answer to the question is (3)(4) = 12
The two dimensions COULD also be (Root1) and (Root24), in which case the answer to the question is (Root24).
Fact 1 is INSUFFICIENT
Fact 2: The perimeter of the rectangle is 14
Perimeter = 2L + 2W = 14
This tells us that L + W = 7
The two dimensions COULD be 3 and 4, in which case the answer to the question is (3)(4) = 12
The two dimensions COULD be 2 and 5, in which case the answer to the question is (2)(5) = 10
Fact 2 is INSUFFICIENT
Combined, we know....
L^2 + W^2 = 25
L + W = 7
Since we cannot have "negative side lengths", we now have a "system" of equations (2 variables and 2 unique equations), so we CAN solve for the two dimensions. With these rules, the dimensions can only be 3 and 4.
Combined, SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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