similar triangles on the gmat
Posted on
02
Feb 2021

Similar Triangles – GMAT Geometry

By: Rich Zwelling (Apex GMAT Instructor)
Date: 2 Feb 2021

One of the most important things to highlight here is that “similar” does not necessarily mean “identical.” Two triangles can be similar without being the same size. For example, take the following:

similar triangles on the GMAT 1

Even though the triangles are of different size, notice that the angles remain the same. This is what really defines the triangles as similar.

Now, what makes this interesting is that the measurements associated with the triangle increase proportionally. For example, if we were to present a triangle with lengths 3, 5, and 7, and we were to then tell you that a similar triangle existed that was twice as large, the corresponding side lengths of that similar triangle would have to be 6, 10, and 14. (This should be no surprise considering our lesson on multiples of Pythagorean triples, such as 3-4-5 leading to 6-8-10, 9-12-15, etc.)

You can also extend this to Perimeter, as perimeter is another one-dimensional measurement. So, if for example we ask:

similar triangles on the GMAT 2

A triangle has line segments XY = 6, YZ = 7, and XZ = 9. If Triangle PQR is similar to Triangle XYZ, and PQ = 18, as shown, then what is the perimeter of Triangle PQR?

Answer: Perimeter is a one-dimensional measurement, just as line segments are. As such, since PQ is three times the length of XY, that means the perimeter of Triangle PQR will be three times the perimeter of Triangle XYZ as well. The perimeter of Triangle XYZ is 6+7+9 = 22. We simply multiply that by 3 to get the perimeter of Triangle PQR, which is 66.

Things can get a little more difficult with area, however, as area is a two-dimensional measurement. If I double the length of each side of a triangle, for example, how does this affect the area? Think about it before reading on…

SCENARIO

Suppose we had a triangle that had a base of 20 and a height of 10:

similar triangles on the GMAT 3

The area would be 20*10 / 2 = 100.

Now, if we double each side of the triangle, what effect does that have on the height? Well, the height is still a one-dimensional measurement (i.e. a line segment), so it also doubles. So the new triangle would have a base of 40 and a height of 20. That would make the area 40*20 / 2 = 400.

Notice that since the original area was 100 and the new area is 400, the area actually quadrupled, even though each side doubled. If the base and height are each multiplied by 2, the area is multiplied by 22. (There’s a connection here to units, since units of area are in square measurements, such as square inches, square meters, or square feet.)

Now, let’s take a look at the following original problem:

Triangle ABC and Triangle DEF are two triangular pens enclosing two separate terrariums. Triangle ABC has side lengths 7 inches, 8 inches, and 10 inches. A beetle is placed along the outer edge of the other terrarium at point D and traverses the entire perimeter once without retracing its path. When finished, it was discovered that the beetle took three times as long as it did traversing the first terrarium traveling at the same average speed in the same manner. What is the total distance, in inches, that the beetle covered between the two terrariums?

A) 25
B) 50
C) 75
D) 100
E) 125

Explanation

This one has a few traps in store. Hopefully you figured out the significance of the beetle taking three times as long to traverse the second terrarium at the same average speed: it’s confirmation that the second terrarium has three times the perimeter of the first. At that point, you can deduce that, since the first terrarium has perimeter 7+8+10 = 25, the second one must have perimeter 25*3 = 75. However, it can be tempting to then choose C, if you don’t read the question closely. Notice the question effectively asks for the perimeters of BOTH terrariums. The correct answer is D.

GMAT Triangle Series Articles:

A Short Meditation on Triangles
The 30-60-90 Right Triangle
The 45-45-90 Right Triangle
The Area of an Equilateral Triangle
Triangles with Other Shapes
Isosceles Triangles and Data Sufficiency
Similar Triangles
3-4-5 Right Triangle
5-12-13 and 7-24-25 Right Triangles

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Posted on
30
Jul 2020

Should you include your GMAT score on your resume?

A lot of our clients ask if having a good GMAT score can help you on a job search. The truth is that for some jobs it can be immensely useful. However, other jobs might not even take a look at it. Ultimately, it’s up to the HR departments of your potential employer. Still, there are some rules of thumb to follow. 

A Really Strong Score

Let me first begin by saying that the only time you should list the GMAT on your resume is if it’s a really strong score. We’re talking 700 or above. There’s no sense talking about a middling or even middling-good GMAT score if you run the risk of having someone ask: “Well why didn’t you score higher?” Really, the bar is about 700. 

There are a lot of industries that really value the GMAT and those are going to largely parallel those that value the MBA. Finance, banking, and consulting firms will generally respond favorably to a GMAT score and one of the things to understand about why this is is to understand what the GMAT is and how it factors into a hiring decision. 

GMAT As a Signal

The GMAT’s what’s called a psychometric exam and much like other standardized tests, whether it’s the SAT, the ACT, GRE, LSAT, these test not just what you know but to varying degrees how you think and many of the top consulting shops have HR departments that have their own in-house tests. So the GMAT serves as a good proxy for those and signals that you will likely thrive and do well in the testing environment that, let’s say, McKinsey might place you in. 

Understand that a strong GMAT score immediately says to the the recruiter, that you can handle a certain amount of intellectual rigor and then you have a certain amount of pliability to the way you think. That’s the value of a GMAT score on a resume, aside from the fact, of course, that it compares you to your peers favorably. 

Include Your GMAT Score Where Necessary

So, as you’re hunting for jobs, whether it’s post-MBA or whether you just took the GMAT and decided not to go to business school or got an alternative degree, think about listing your GMAT and think about it as a talking point for how you overcame an obstacle or in a way that might be complementary to the profile or the narrative that you’re trying to present to a particular hiring manager. I hope this helps and if you have any questions don’t hesitate to contact us!

If you enjoyed this video, you can find more useful GMAT content such as: Everything you need to know about the GMAT and GMAT Prep Tips

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