• Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • examPAL
    Most awarded test prep in the world
    Now free for 30 days

    Available with Beat the GMAT members only code

    MORE DETAILS
    examPAL

OG 13 128

This topic has 4 expert replies and 1 member reply
oquiella Master | Next Rank: 500 Posts Default Avatar
Joined
12 May 2015
Posted:
164 messages
Upvotes:
3

OG 13 128

Post Tue Dec 22, 2015 3:34 pm
The hypotenuse of a right triangle is 10cm. What is the perrimeter, in centimeters, of the triangle?


1. The area of the triangle is 25 square cetimeters
2. The 2 legs of the triagle are of equal length.


Answer: D


Please explain reasoning

  • +1 Upvote Post
  • Quote
  • Flag
Post Wed Jan 03, 2018 7:41 am
oquiella wrote:
The hypotenuse of a right triangle is 10cm. What is the perrimeter, in centimeters, of the triangle?

1. The area of the triangle is 25 square cetimeters
2. The 2 legs of the triagle are of equal length.
We are given that the hypotenuse of a right triangle is 10 cm and we need to determine the perimeter of the triangle. We can let the other two sides (i.e., the two legs) of the right triangle be a and b. Since it’s a right triangle, by the Pythagorean theorem, we have a^2 + b^2 = 10^2, or a^2 + b^2 = 100. If we can find the values of a and b, then we can determine the perimeter of the triangle, since it will be a + b + 10.

Statement One Alone:

The area of the triangle is 25 square centimeters.

We are given a right triangle and we’ve let the two non-hypotenuse sides be a and b. Recall that the two non-hypotenuse sides of a right triangle are actually the base and height of the triangle, so the area of this triangle is A = ab/2. From the aforementioned equation a^2 + b^2 = 100, we can solve b as b = √(100 - a^2). Since we are given that A = 25, and substituting b = √(100 - a^2) in A = ab/2, we can say:

25 = [a√(100 - a^2)]/2

We see that we can solve for a (though we don’t have to actually solve for it). And once we’ve solved for a, we can determine the value of b, since b = √(100 - a^2). Therefore, we can determine the perimeter of the triangle, since we can determine the values of both a and b. Statement one alone is sufficient to answer the question.

Statement Two Alone:

The 2 legs of the triangle are of equal length.

Since a^2 + b^2 = 100 and we are given that a = b, we can say:

a^2 + a^2 = 100

We see that we can solve for a (though we don’t have to actually solve for it). And once we’ve solved for a, we can determine the value of b, since b = a. Therefore, we can determine the perimeter of the triangle, since we can determine the values of both a and b. Statement two alone is sufficient to answer the question.

Answer: D

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Wed Dec 23, 2015 3:53 pm
Quote:
The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle?

(1) The area of the triangle is 25 square centimeters.
(2) The 2 legs of the triangle are of equal length
Plugging in numbers might be challenging, because we'd need to find values that satisfy BOTH the given information (hypotenuse = 10) AND the information in the statements.

IMPORTANT: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or length into having just one value. This concept is discussed in much greater detail in our free video: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1103

So, for this question, if a statement FORCES our right triangle into having ONE AND ONLY ONE shape and size, then that statement is sufficient. Moreover, we NEED NOT find the actual perimeter of the triangle. We need only recognize that we could find its perimeter (finding the perimeter will just waste time).

Okay, onto the question....

Target question: What is the perimeter of the right triangle?

Given: The hypotenuse of the triangle has length 10 cm.

Statement 1: The area of the triangle is 25 square centimeters.
Let's let x = length of one leg
Also, let y = length of other leg
So, if the area is 25, we can write (1/2)xy = 25 [since area = (1/2)(base)(height)]
Multiply both sides by 2 to get xy = 50
Multiply both sides by 2 again to get 2xy = 100 [you'll soon see why I performed this step]


Now let's deal with the given information (hypotenuse has length 10)
The Pythagorean Theorem tells us that x² + y² = 10²
In other words, x² + y² = 100

We now have two equations:
2xy = 100
x² + y² = 100

Since both equations are set equal to 100, we can write: 2xy = x² + y²

Rearrange this to get x² - 2xy + y² = 0
Factor to get (x - y)(x - y) = 0
This means that x =y, which means that the two legs of our right triangle HAVE EQUAL LENGTH.

So, the two legs of our right triangle have equal length AND the hypotenuse has length 10.
There is only one such right triangle in the universe, so statement 1 FORCES our right triangle into having ONE AND ONLY ONE shape and size.

This means that statement 1 is SUFFICIENT

Statement 2: The 2 legs of the triangle are of equal length
We already covered this scenario in statement 1.
So, statement 2 is also SUFFICIENT

Answer = D

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Marty Murray Legendary Member
Joined
03 Feb 2014
Posted:
2050 messages
Followed by:
131 members
Upvotes:
955
GMAT Score:
800
Post Tue Dec 22, 2015 9:35 pm
Quote:
The hypotenuse of a right triangle is 10cm. What is the perimeter, in centimeters, of the triangle?

1. The area of the triangle is 25 square centimeters
2. The 2 legs of the triangle are of equal length.
The perimeter of the triangle = the total of the lengths of the three sides of the triangle, a + b + c. Since we already know the length of the hypotenuse, c, we just need either a and b, or a + b to calculate the perimeter.

Statement 1:

Since we know that c = 10, we know that a² + b² = 100

The area is 25, and the triangle is a right triangle. So a and b can be the height and base.

So, we know that ab/2 = 25.

So ab = 50.

We can can combine what we have to get the following.

a² + 2ab + b² = 200 --> (a + b)² = 200

So a + b = √200 and we have the answer to the rephrased question.

NOTICE, that while we don't have a or b, we know that a + b + c is √200 + 10.

Sufficient.

Statement 2:

From Statement 2 we know that a = b.

So we can use a² + a² = c² = 100 to calculate the lengths of a and b and answer the rephrased question.

Sufficient.

The correct answer is D.

_________________
Marty Murray
GMAT Coach
m.w.murray@hotmail.com
https://infinitemindprep.com/
In Person in the New York Area and Online Worldwide

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Wed Dec 23, 2015 5:02 am
oquiella wrote:
The hypotenuse of a right triangle is 10cm. What is the perrimeter, in centimeters, of the triangle?

1. The area of the triangle is 25 square cetimeters
2. The 2 legs of the triangle are of equal length.
Start with statement 2, which seems easier to evaluate.

Statement 2:
A right triangle with 2 equal legs is an ISOSCELES right triangle.
In an isosceles right triangle, the sides are in the following ratio:
x : x : x√2.

The prompt indicates that the hypotenuse has a length of 10.
Since x√2 = 10, we get:
x = 10/√2.

Thus, the triangle has a base and height of 10/√2 and a hypotenuse of 10.
Since the lengths of all 3 sides are known, the perimeter can be determined.
SUFFICIENT.

Statement 1:
Since the two statements cannot contradict each other, it must be possible that the triangle implied by statement 2 also satisfies statement 1.
Thus, an area of 25 MUST be yielded by a right triangle with a base and height of 10/√2 and a hypotenuse of 10.
Proof:
If b = 10/√2 and h = 10/√2, then A = (1/2)bh = (1/2)(10/√2)(10/√2) = 25.

Check whether a DIFFERENT right triangle with a hypotenuse of 10 can also yield an area of 25.
A common right triangle with a hypotenuse of 10 is a 6-8-10 triangle.
The area of a 6-8-10 triangle = (1/2)(6)(8) = 24.
Doesn't work.
Implication:
For a right triangle with a hypotenuse of 10 to yield an area of 25, it MUST have a base and height of 10/√2.

Since the lengths of all 3 sides are known, the perimeter can be determined.
SUFFICIENT.

The correct answer is D.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.



Last edited by GMATGuruNY on Thu Dec 24, 2015 5:38 am; edited 1 time in total

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

Post Wed Dec 23, 2015 9:30 am
Hi oquiella,

One of the interesting things about the GMAT is that most questions can be approached in a few different ways, so it is beneficial to be a "strong thinker" on Test Day. Knowing how to do math is sometimes what's needed (although sometimes the math can be done in several different ways); in other situations, the ability to figure out patterns is what's needed.

Whoever wrote this explanation is taking a real heavy "math" approach to the problem, which is fine. I think you'll find this next approach to be a bit easier…

The prompt tells us that the hypotenuse of a right triangle is 10. The question asks us for the perimeter, so we're going to need the lengths of the other two sides.

Since we have a right triangle, we can use the Pythagorean Theorem:

X^2 + Y^2 = 10^2

**Important: triangles can't have "negative" sides, so both X and Y MUST be positive.**

We have 2 variables, but only 1 equation, so we can't figure out the exact values of X and Y

Fact 1: Triangle area = 25

Since Area = (1/2)(B)(H) we know that….

(1/2)(X)(Y) = 25
(X)(Y) = 50

Now we have ANOTHER equation. Combined with what we were given in the beginning, we have…

Two variables AND two UNIQUE equations, which means we have a "system" of equations and we CAN solve for X and Y. No more math is needed.
Fact 1 is SUFFICIENT.

Fact 2: The two legs of the triangle are equal.

Now we know that X = Y.

This gives us a SECOND equation to work with. Just as in Fact 1, we have a "system" and we can solve for X and Y.
Fact 2 is SUFFICIENT

Final Answer: D

Be on the lookout for "system" questions. You'll see a couple on Test Day and they're built around some useful math "patterns" that you can use to avoid doing work.

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 lheiannie07 108 topics
2 ardz24 67 topics
3 Roland2rule 63 topics
4 LUANDATO 53 topics
5 swerve 46 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

143 posts
2 image description Jeff@TargetTestPrep

Target Test Prep

119 posts
3 image description Rich.C@EMPOWERgma...

EMPOWERgmat

116 posts
4 image description Scott@TargetTestPrep

Target Test Prep

101 posts
5 image description Max@Math Revolution

Math Revolution

86 posts
See More Top Beat The GMAT Experts