prasannar wrote:
If the area of triangular region RST is 25, what is the perimeter of RST?
(1) The length of one side of RST is \(5\sqrt{2}\).
(2) RST is a right isosceles triangle.
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Assume b is the base and h is the height of the triangle.
(1/2)bh = 25.
Since we have 2 variables and 1 equation, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1)
Since there two cases, we can't determine the perimeter of RST.
We don't know which side is 5√2.
Those cases are b is 5√2 or another side length is 5√2.
This is not sufficient.
Condition 2)
Assume that the length of two legs is a.
The area of the right isosceles triangle is (1/2)a^2 = 25.
Then a = 5 and the hypotenuse is 5√2 .
The perimeter is 10 + 5√2.
Condition 2) is sufficient.
Therefore, the answer is B.
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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