GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Aug 2020, 11:46

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

The two sides of a right triangle are 12 and 15. Which one of the foll

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65807
The two sides of a right triangle are 12 and 15. Which one of the foll  [#permalink]

Show Tags

02 Jul 2020, 01:39
00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:20) correct 42% (01:29) wrong based on 30 sessions

HideShow timer Statistics

The two sides of a right triangle are 12 and 15. Which one of the following can be the length of the third side?

I. 9

II. $$3\sqrt{41}$$

III. 20

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

_________________
Manager
Joined: 12 Oct 2019
Posts: 55
Re: The two sides of a right triangle are 12 and 15. Which one of the foll  [#permalink]

Show Tags

02 Jul 2020, 01:46
Hypotenuse is the longest side of a right angled triangle.

So, there are two triangles possible.
Case 1

Base = 12 and Perpendicular = 15
Third side = Hypotenuse $$= \sqrt{15^2 + 12^2} = \sqrt{225 + 144} = \sqrt{369}$$

Hypotenuse = $$\sqrt{3^2 \times 41} = 3 \times \sqrt{41}$$

Case 2

Hypotenuse = 15 and one of the Base or perpendicular = 12.

Third Side $$= \sqrt{15^2 - 12^2} = \sqrt{225 - 144} = \sqrt{81} = 9$$

OA, C
Bunuel wrote:
The two sides of a right triangle are 12 and 15. Which one of the following can be the length of the third side?

I. 9

II. $$3\sqrt{41}$$

III. 20

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
Director
Joined: 16 Feb 2015
Posts: 657
Location: United States
Re: The two sides of a right triangle are 12 and 15. Which one of the foll  [#permalink]

Show Tags

02 Jul 2020, 02:01
Explanation:

Let H=15, B or P=12
So, H^2 = B^2 + P^2
225 = 144 + P^2
P^2 = 81
P = 9

Let B=12, P=15 ,H=?
So, H^2 = B^2 + P^2
H^2 = 144 + 225
H^2 = 369
H = 3√41
Option 1 & 2 Satisfies

IMO-C
RC Moderator
Joined: 05 May 2016
Posts: 355
Location: India
Re: The two sides of a right triangle are 12 and 15. Which one of the foll  [#permalink]

Show Tags

05 Jul 2020, 05:48
Bunuel wrote:
The two sides of a right triangle are 12 and 15. Which one of the following can be the length of the third side?

I. 9

II. $$3\sqrt{41}$$

III. 20

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

Given sides: 12 , 15
Given Triangle: Right angled.

Possible Combinations:

1. 12, 15 are given we calculate the hypotenuse.
=> $$\sqrt{12^2 + 15^2}$$ = $$\sqrt{369}$$ = $$3\sqrt{41}$$
=> II could be one of the sides.

2. we let 15 be the hypotenuse, and calculate the other side.
=> $$\sqrt{15^2 - 12^2}$$ = $$\sqrt{81}$$ = 9.
=> I could also be a side.

But III can never be a side, since the largest side of the triangle could either be 15 or $$3\sqrt{41}$$.

Manager
Status: BELIEVE IN YOURSELF
Joined: 06 Oct 2019
Posts: 98
Location: India
The two sides of a right triangle are 12 and 15. Which one of the foll  [#permalink]

Show Tags

05 Jul 2020, 07:13
Bunuel wrote:
The two sides of a right triangle are 12 and 15. Which one of the following can be the length of the third side?

I. 9

II. $$3\sqrt{41}$$

III. 20

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

The simplest way to solve is the use of Pythagoras theorem

As the 2 sides given 12 and 15 the other side either be smaller than 15 or greater than 15.

if it is less than 15, it acts as either height or base of the triangle and if it is greater than 15, it acts as the hypotenuse of the triangle.

I. 9 less than 15

$$\sqrt{9^2+12^2}$$ check if you are getting 15 (YES)

II. $$3\sqrt{41}$$ =18 approx which is greater than 15

$$\sqrt{15^2+12^2}$$ check if you are getting $$3\sqrt{41}$$ (YES)

III. 20 is also greater than 15 which obviously gonna be incorrect because we already found out in II option, $$\sqrt{15^2+12^2}$$ cannot be equal to 20

GMAT Club Legend
Status: GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator l A motivator and an Optimist :)
Joined: 08 Jul 2010
Posts: 4521
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
The two sides of a right triangle are 12 and 15. Which one of the foll  [#permalink]

Show Tags

05 Jul 2020, 08:05
Bunuel wrote:
The two sides of a right triangle are 12 and 15. Which one of the following can be the length of the third side?

I. 9

II. $$3\sqrt{41}$$

III. 20

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

Property: Sum of any two sides of ∆ > Third Side of the ∆

Two sides are 12 and 15

If third side (x) is longest then, 12+15 > x i.e. x < 27

If third side (x) is NOT longets then, 12+x > 15 i.e. x > 3

i.e. 3 < x < 27

Point to note: Triangle given here is a right triangle

Case 1: $$12^2 + 15^2 = x^2$$ i.e $$x = 3√41$$

Case 2: $$12^2 + x^2 = 15^2$$ i.e $$x = 9$$

I. 9 POSSIBLE

II. $$3\sqrt{41}$$ POSSIBLE

III. 20 NOT POSSIBLE

_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Intern
Joined: 15 Apr 2014
Posts: 1
The two sides of a right triangle are 12 and 15. Which one of the foll  [#permalink]

Show Tags

05 Jul 2020, 08:24
By pythogoras theorem
Sum of squares of perpendicular and base is equal to hypotenuse square.

Case one when both 12 and 15 are perpendicular and base then the third side hypotenuse will be option 2. And in other case when 15 I'd hypotenuse then the three sides will be 12,9 and 15.
So both 1 and 2 are correct

Posted from my mobile device
The two sides of a right triangle are 12 and 15. Which one of the foll   [#permalink] 05 Jul 2020, 08:24