Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 04:46

### GMAT Club Daily Prep

#### 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

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

# Two congruent triangles were combined in three different ways, as show

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56306
Two congruent triangles were combined in three different ways, as show  [#permalink]

### Show Tags

18 Sep 2016, 10:02
00:00

Difficulty:

45% (medium)

Question Stats:

74% (02:40) correct 26% (02:42) wrong based on 95 sessions

### HideShow timer Statistics

Two congruent triangles were combined in three different ways, as shown above. If the perimeters of the shapes above are 12, 14, and 16, then what is the perimeter of one triangle?

A. 13/2
B. 14/2
C. 21/2
D. 22/2
E. 42/3

Attachment:

T88922.png [ 3.02 KiB | Viewed 1743 times ]

_________________
Manager
Joined: 05 Jun 2015
Posts: 78
Location: United States
WE: Engineering (Transportation)
Re: Two congruent triangles were combined in three different ways, as show  [#permalink]

### Show Tags

18 Sep 2016, 18:47
3
Let sides of each of the triangle be a, b and c.
Perimeters of the combined shapes are given. In each of the shapes, only two sides contribute to the perimeter as the third side is in the interior.

$$2(a+b) =12$$
$$2(b+c) = 14$$
$$2(c+a) = 16$$

Adding, $$4 (a+b+c) = 42$$
$$a+b+c = \frac{21}{2}$$

Option C
Intern
Joined: 05 Sep 2015
Posts: 43
Two congruent triangles were combined in three different ways, as show  [#permalink]

### Show Tags

19 Sep 2016, 05:11
Given that the two triangles are congruent we can name their sides as a, b and c. It doesn't really matter how you choose to label the sides, but let's go with a=height (short base), b=long base, c=hypotenuse.

Based on this the perimeter of the shapes resulting from combining the triangles in different ways (as shown in the figure) is

Rectangle (two long bases, two heights): 2a + 2b = 12,

Parallelogram on top right of the figure (two short heights, two hypotenuses): 2a + 2c = 14 and

Bottom parallelogram (two long bases, two hypotenuses): 2b + 2c = 16.

We could use these three equations to find the individual values of a,b and c, but we don't really need to - we're looking for the perimeter of the triangle, which is the expression a+b+c. To find the value of that expression, add all three equations to get

4a + 4b + 4c = 42

--> 4(a + b + c) = 42

--> a + b + c = 42/4 = 21/2.

Hence, the perimeter of one triangle is 21/2.
Non-Human User
Joined: 09 Sep 2013
Posts: 11719
Re: Two congruent triangles were combined in three different ways, as show  [#permalink]

### Show Tags

18 Mar 2019, 01:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Two congruent triangles were combined in three different ways, as show   [#permalink] 18 Mar 2019, 01:59
Display posts from previous: Sort by