• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

# What is the perimeter of a certain right triangle?

tagged by: AAPL

00:00

A

B

C

D

E

## Global Stats

Difficult

What is the perimeter of a certain right triangle?

(1) The hypotenuse's length is 10
(2) The triangle's area is 24

The OA C.

The trick with this question is that in statement 1 we cannot actually assume that the sides are 6 and 8 just because we know that
x^2 +y^2 = 100

We cannot make any assumptions about X and Y UNLESS there is a restriction such as "X and Y must be integers" or "The product of XY is 48."

Hence, the correct answer is C.

Has anyone another strategic approach to solving this DS question? Regards!

### Top Member

Legendary Member
Joined
02 Mar 2018
Posted:
525 messages
Followed by:
1 members
Perimeter of a triangle = Side a + Side b + Side c
However, if we have 2 known sides we can find the third side with Pythagoras theories before calculating the perimeter.

Statement 1 = The hypotenuse length is 10
Given that hypotenuse = 10
Let opposite and adjacent be a and b respectively.
From Pythagoras theories; we have
$$10^2\ =\ a^2\ +\ b^2$$
$$100\ =\ a^2\ +\ b^2$$
The given information is not enough to find the perimeter of the triangle, hence statement 1 is INSUFFICIENT.

Statement 2 = The triangle's are is 24
$$Area\ of\ triangle\ =\ \frac{1}{2}\ \cdot\ base\ \cdot\ height.$$
$$=\ \frac{1}{2}\ \cdot\ opposite\ \cdot\ adjacent.$$
$$=\ \frac{1}{2}\ \cdot\ a\ \cdot\ b.$$
$$24=\ \frac{1}{2}\ \cdot\ a\ \cdot\ b.$$
$$24=\ \frac{ab}{2}$$
$$ab\ =\ 48$$
This does not provide us with information on any of the sides, hence Statement 2 is INSUFFICIENT.

Combining Statement 1 and 2 together =
$$a^2\ +\ b^2\ =100\ -\ Statement\ 1$$
$$ab=48\ -\ Statement\ 2$$
From Statement 1
$$a^2\ +\ b^2\ =\ 100$$
$$a^2\ +\ b^2\ can\ bw\ written\ as\ \left(a\ +\ b\right)^2$$
$$\left(a\ +\ b\right)^2\ =\ \left(a\ +\ b\right)\cdot\left(a\ +\ b\right)$$
$$=\left(a\ \cdot\ a\right)\ +\left(a\ \cdot b\right)+\left(b\ \cdot\ a\right)+\ \left(b\cdot b\right)$$
$$=a^2\ +\ b^2\ +\ 2ab$$
$$From\ Statement\ 1\ a^2\ +\ b^2\ =100$$
$$From\ Statement\ 2\ \ ab=\ 48$$
$$\left(a\ +\ b\right)^2\ =\ \left(a^{2\ }+b^2\right)+\ \left(2ab\right)$$
$$=\ \left(100\right)\ +\ \left(2\ \cdot\ 48\right)$$
$$=\ 100\ +\ 96$$ $$=196$$
$$\sqrt{\left(a\ +\ b\right)^2}=\sqrt{196}$$
$$a\ +\ b\ =\ 14$$
We already have hypotenuse as 10
Opposite and adjacent as a + b = 14
Perimeter = (a + b ) + 10
=14 + 10
= 24
Option C is CORRECT.

### GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
523 messages
Followed by:
25 members
59
AAPL wrote:
What is the perimeter of a certain right triangle?

(1) The hypotenuse's length is 10
(2) The triangle's area is 24

Has anyone another strategic approach to solving this DS question? Regards!
Sure! The key point is to understand we are looking for the uniqueness (or not) of numerical values, not explicit calculations!
(Our method has this important detail in its "backbone" when dealing with ANY Data Sufficiency problem... especially in Geometry-related ones!)

$right\,\,\Delta \,\,\,:\,\,\,a \leqslant b < c\,\,\,{\text{sides}}\,\,\,\,\,$
$?\,\, = \,\,{\text{peri}}{{\text{m}}_{\,\Delta }}$

$\left( 1 \right)\,\,\,{\text{c}} = 10\,\,\,\,\,::\,\,\,\,{\text{GEOMETRIC}}\,\,{\text{BIFURCATION}}\,\,\,\,\,\,\left( {{\text{see}}\,\,{\text{image}}\,\,{\text{attached}}} \right)\,\,$

$\left( 2 \right)\,\,\,{S_\Delta } = 24\,\,\,\left\{ \begin{gathered} \,\left( {a,b,c} \right) = \left( {3 \cdot 2\,\,,4 \cdot 2\,\,,\,\,5 \cdot 2} \right)\,\,\,\,\,\,\left[ {3k,4k,5k} \right]\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,?\,\,\, = \,\,\,2\left( {3 + 4 + 5} \right) = 24 \hfill \\ \,\left( {a,b,c} \right) = \left( {\sqrt {2 \cdot 24} \,\,,\sqrt {2 \cdot 24} \,\,,\,\,\sqrt {2 \cdot 24} \, \cdot \sqrt 2 } \right)\,\,\,\,\,\,\,\,\,\left[ {L,L,L\sqrt 2 } \right]\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,?\,\,\, \ne \,\,24 \hfill \\ \end{gathered} \right.$

$\left( {1 + 2} \right)\,\,24 = \frac{{10 \cdot h}}{2}\,\,\,\,\, \Rightarrow \,\,\,\,h\,\,\,{\text{unique}}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {{\text{see}}\,\,{\text{image}}\,\,{\text{attached}}} \right)} \,\,\,\,\Delta \,\,\,unique\,\,\,\left( {{\text{but}}\,\,{\text{congruents!}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,?\,\, = \,\,{\text{peri}}{{\text{m}}_{\,\Delta }}\,\,\,{\text{unique}}$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 30/Sep with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 70% discount!

### Top First Responders*

1 Jay@ManhattanReview 83 first replies
2 Brent@GMATPrepNow 68 first replies
3 fskilnik 55 first replies
4 GMATGuruNY 36 first replies
5 ceilidh.erickson 13 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik

GMAT Teacher

199 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

160 posts
3 Scott@TargetTestPrep

Target Test Prep

109 posts
4 Jay@ManhattanReview

Manhattan Review

95 posts
5 GMATGuruNY

The Princeton Review Teacher

90 posts
See More Top Beat The GMAT Experts