Hi All,
We're asked for the perimeter of rectangle ABCD. To answer this question, we'll need to figure out the Length (L) and Width (W) of the rectangle. This prompt involves a great 'System Algebra' shortcut that you can use to avoid doing a lot of math.
1) The longer side of the rectangle is 2 meters shorter than its diagonal
With the information in Fact 1, we can create 2 equations (with the diagonal represented by D):
L = D - 2
L^2 + W^2 = D^2
Unfortunately, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter.
Fact 1 is INSUFFICIENT
2) The ratio of the shorter side to the diagonal is 1/3
With the information in Fact 2, we can create 2 equations (one of which is the same as we created in Fact 1):
W/D = 1/3....... D = 3W
L^2 + W^2 = D2
Again, with 3 unknowns, but only 2 equations, we cannot solve for any of the variables, so we cannot figure out the perimeter.
Fact 2 is INSUFFICIENT
Combined, we know that we're dealing with a rectangle, so the variables can ONLY be POSITIVE numbers. As such, even though we're dealing with 'squared terms', the negative answers are not possible here. We have 3 variables and 3 unique equations, so we CAN solve for all 3 variables - and there will be just one solution.
Combined, SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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