Source: Official Guide Revised GRE 1st Ed. Part 6; Set 3; #1

21

In the figure above, ABCD is a parallelogram

In the figure above, ABCD is a parallelogram. Quantity A : The area of ABCD Quantity B : 24 Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

2 Explanations

1

Roshan Shrestha

I also want to show that the area is less than 24 by drawing an altitude to the side 6 instead of 4. Can you please suggest me how to do that ? Thanks

Jan 20, 2017 • Comment

Sam Kinsman, Magoosh Tutor

Hi Roshan,

Yes, it would be possible to do that - but we would need to use trigonometry (sine, cosine, or tangent) - and those functions aren't available on the GRE calculator. So we cannot solve it this way. Let me explain why we'd need to use trigonometry! :)

Let's say we draw the height, from point D to line BC, so that the height makes a right angle with BC. The height also makes a right angle with AD.

Let's call the point where the height intersects BC point X. So we have a triangle now: DXC. We know that inside the triangle, angle D is (125-90=35). Angle X is 90, so angle C must be (180-90-35=55).

So we have a triangle with angles 35, 90, and 55. We also know one side: DC is 6.

From here, to find the length of DX (the height), we would need to use sine, cosine, or tangent. If we only know the length of one side, cannot find the length of another side without using trigonometry. (Of course, the exception is when we have a special triangle - but this is not one of the special triangles you need to memorize).

So on the GRE, you cannot solve this problem using the method you suggested, since we don't have a calculator with trig buttons.

Jan 20, 2017 • Reply

5

Gravatar Chris Lele, Magoosh Tutor

Oct 7, 2012 • Comment

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