makkiemaps wrote:Anurag@Gurome wrote:(1) By Pythagoras Theorem, (3√2)^2 = Y^2 + 3^2 implies Y = √(18 - 9) = √9 = 3
This implies it is a 45-45-90 triangle.
Hence, the given info is SUFFICIENT.
(2) We are not given that one of the angles is 90º (as the right angle symbol is missing from the figure, so I am assuming that this is not a right angled triangle), it is just given that it is an isosceles triangle.
Hence, the given info is NOT SUFFICIENT.
(3) Again we are not given that one of the angles is 90º (as the right angle symbol is missing from the figure, so I am assuming that this is not a right angled triangle), so we cannot find the remaining two angles and the 3rd side.
Hence, the given info is NOT SUFFICIENT.
Thanks for the detailed explanation, I have a doubt in (2)
2. Here three sides are given as 3, 3, 3√2. Using ratios, can't we say that angles are 90,45,45?
Given three 3 sides of a triangle -- even one without a right angle -- we can determine the degree measurement of each angle by using the Law of Cosines. While the Law of Cosines is beyond the scope of the GMAT, we should recognize that knowing all 3 sides is sufficient information to determine all 3 angles. The reverse, however, is not true: if we know all 3 angles, we still need to know the length of at least one side in order to determine the lengths of the other 2.
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