Triangle DS

[yellowho]

I just made up these 3 quick problems. Is there enough info. to solve for what is asked in each?

[makkiemaps]

The first two are really simple:

1. By applying Pythagoras theorem, its an isosceles triangle, so angles are 90, 45, 45.

2. Again the angles are 90, 45, 45

3. And if we apply T -ratios here, tan 60 = root(3). Hence angles are 30, 60, 90, Hypotenuse is 6

[Anurag@Gurome]

(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) 3, 3, and 3√2 implies that the triangle is a right angled triangle as (3√2)^2 = 3^2 + 3^2 is true.
Hence, the given info is SUFFICIENT.

(3) 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.

[makkiemaps]

(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?

[Anurag@Gurome]

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?

You are right, that would form a Pythagorean Triplet, thanks for noticing that. I have edited my previous post.

[GMATGuruNY]

(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.

[makkiemaps]

(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.

Right, coz in case of unknown angles we have the extra information that their sum=180 deg.