Geo

[artstudent]

Why do you need B in this?

If you draw a line down from the 120. You have a perpendicular line. The 120 angle is split into 90 and 30. Thus the triangle is 30,60,90. Can you not do that?

[Anurag@Gurome]

Why do you need B in this?

If you draw a line down from the 120. You have a perpendicular line. The 120 angle is split into 90 and 30. Thus the triangle is 30,60,90. Can you not do that?

Area of a trapezoid = (1/2) * b1 * b2 * h, where b1 = base 1, b2 = base 2, and h = height between the two bases. We know that h = 4.
The way you said, we drop a perpendicular from B on DC so that it meets DC at E. Then angle ABE = 90º, angle EBC = 30º, angle BEC = 90º, and angle ECB = 60º. This means triangle BEC is 30-60-90 triangle. So, the sides are in the ratio 1 : 2 : √3.
BE = 4 implies we can find EC. Now we need to find ED and AB.

(1) AB = 5 but still we don't know ED (we are not given that the given trapezoid is an isosceles trapezoid); NOT sufficient.

(2) angle ADC = 60º implies that the given trapezoid is an isosceles trapezoid. Let us drop a perpendicular from A on DC so that it meets DC at F. We can find EC from the main question and EC = DF. FE = AB, but we don't know AB; NOT sufficient.

Combining (1) and (2) we know AB and ED. Hence SUFFICIENT.

The correct answer is C.

[artstudent]

AB is not parallel with CD?

Why do you need B in this?

If you draw a line down from the 120. You have a perpendicular line. The 120 angle is split into 90 and 30. Thus the triangle is 30,60,90. Can you not do that?

Area of a trapezoid = (1/2) * b1 * b2 * h, where b1 = base 1, b2 = base 2, and h = height between the two bases. We know that h = 4.
The way you said, we drop a perpendicular from B on DC so that it meets DC at E. Then angle ABE = 90º, angle EBC = 30º, angle BEC = 90º, and angle ECB = 60º. This means triangle BEC is 30-60-90 triangle. So, the sides are in the ratio 1 : 2 : √3.
BE = 4 implies we can find EC. Now we need to find ED and AB.

(1) AB = 5 but still we don't know ED (we are not given that the given trapezoid is an isosceles trapezoid); NOT sufficient.

(2) angle ADC = 60º implies that the given trapezoid is an isosceles trapezoid. Let us drop a perpendicular from A on DC so that it meets DC at F. We can find EC from the main question and EC = DF. FE = AB, but we don't know AB; NOT sufficient.

Combining (1) and (2) we know AB and ED. Hence SUFFICIENT.

The correct answer is C.

[Anurag@Gurome]

AB is not parallel with CD?

Why do you need B in this?

If you draw a line down from the 120. You have a perpendicular line. The 120 angle is split into 90 and 30. Thus the triangle is 30,60,90. Can you not do that?

Area of a trapezoid = (1/2) * b1 * b2 * h, where b1 = base 1, b2 = base 2, and h = height between the two bases. We know that h = 4.
The way you said, we drop a perpendicular from B on DC so that it meets DC at E. Then angle ABE = 90º, angle EBC = 30º, angle BEC = 90º, and angle ECB = 60º. This means triangle BEC is 30-60-90 triangle. So, the sides are in the ratio 1 : 2 : √3.
BE = 4 implies we can find EC. Now we need to find ED and AB.

(1) AB = 5 but still we don't know ED (we are not given that the given trapezoid is an isosceles trapezoid); NOT sufficient.

(2) angle ADC = 60º implies that the given trapezoid is an isosceles trapezoid. Let us drop a perpendicular from A on DC so that it meets DC at F. We can find EC from the main question and EC = DF. FE = AB, but we don't know AB; NOT sufficient.

Combining (1) and (2) we know AB and ED. Hence SUFFICIENT.

The correct answer is C.

AB is parallel to CD as in a quadrilateral with one pair of parallel sides is referred to as a trapezoid. But it is not given in the main question that it is an isosceles trapezoid.

[GmatKiss]

IMO:C