What is the length of line segment $AB$ in the figure

Expert replies

Previous Topic Next Topic

AAPL: Moderator; Posts: 2651; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Mon Jul 08, 2019 2:05 pm

Timer

00:00

Answers

Stats

Difficulty—

Economist GMAT

What is the length of line segment $AB$ in the figure above?

A. $\frac{\sqrt{2}}{2}$

B. $\frac{\sqrt{3}}{2}$

C. $\sqrt{2}$

D. $\frac{3}{2}$

E. $\sqrt{3}$

OA C

Like this post

Source: Beat The GMAT — Problem Solving | Mon Jul 08, 2019 2:05 pm

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Tue Jul 09, 2019 7:02 am

If we draw a vertical height from A down to BC, that divides the triangle into a 45-45-90 triangle on the left, and a 30-60-90 triangle on the right. The hypotenuse of the 45-45-90 is AC, so is of length 1, and the height we've drawn is thus of length 1/âˆš2 = âˆš2/2 (since the sides of a 45-45-90 are in a 1 to 1 to âˆš2 ratio). This is opposite the 30 degree angle in the 30-60-90 triangle, so it is the shortest side of that triangle, and the longest side AB is twice as long (since in a 30-60-90 triangle, sides are in a 1 to âˆš3 to 2 ratio), so the length of AB is 2(âˆš2/2) = âˆš2.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Jul 11, 2019 6:51 pm

AAPL wrote:Economist GMAT

What is the length of line segment $AB$ in the figure above?

A. $\frac{\sqrt{2}}{2}$

B. $\frac{\sqrt{3}}{2}$

C. $\sqrt{2}$

D. $\frac{3}{2}$

E. $\sqrt{3}$

OA C

If we drop a perpendicular from vertex A to side BC, that is, if we draw the height, we will divide the triangle into two special right triangles: a 45-45-90 triangle on the left and a 30-60-90 triangle on the right. Let's call this height AD; that is, D is a point on BC such that AD is perpendicular to BC.

We know that the side ratio of a 45-45-90 triangle is x : x : xâˆš2. Since AC = 1, we see that if we let AD = x, then xâˆš2 = 1. So x = 1/âˆš2 = âˆš2/2 = AD.

We also know that the side ratio of a 30-60-90 triangle is x : xâˆš3 : 2x. Since AD = âˆš2/2, we see that AB must be twice as much. So AB = 2(âˆš2/2) = âˆš2.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review