Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th.
Re: In quadrilateral ABCD above, what is the length of AB ?
[#permalink]
Show Tags
27 Apr 2019, 17:03
Hi All,
We're asked for the length of AB in quadrilateral ABCD.
When dealing with 'weird' shapes, it often helps to break the shape down into 'pieces' that are easier to deal with. Here, if you draw a line from B to D, you will from 2 RIGHT TRIANGLES.
Triangle BCD has legs of 3 and 4, so it's a 3/4/5 right triangle. Triangle BAD then has a leg of 1 and a hypotenuse of 5. We can use the Pythagorean Formula to find the missing leg...
1^2 + B^2 = 5^2 1 + B^2 = 25 B^2 = 24
From here, if we square-root both sides, we'll have... B = √24 B = 2√6
If we focus on the blue right triangle, we can EITHER recognize that legs of length 3 and 4 are part of the 3-4-5 Pythagorean triplet, OR we can apply the Pythagorean Theorem.
Either way, we'll see that the triangle's hypotenuse (BD) must have length 5
Now, when we focus on the red right triangle, we can . . .
. . . apply the Pythagorean Theorem to write: x² + 1² = 5² Simplify: x² + 1 = 25 So: x² = 24 So: x = √24 = √[(4)(6)] = (√4)(√6) = 2√6
If we draw diagonal BD, we’ve created two right triangles: BCD and BAD. We see that triangle BCD is a 3-4-5 right triangle. So we see that side BD = 5.
Therefore, triangle BAD is a right triangle with a leg of 1 and a hypotenuse of 5. We can let side AB = n and use the Pythagorean theorem to determine n.