It is currently 19 Dec 2018, 03:48
My Tests

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

GRE Math Challenge #34-the area of an isosceles triangle

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4756
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1668 [0], given: 396

CAT Tests
GRE Math Challenge #34-the area of an isosceles triangle [#permalink] New post 09 Sep 2014, 01:17
Expert's post
00:00

Question Stats:

53% (01:10) correct 46% (01:03) wrong based on 13 sessions
Which of the folllowing could be the area of an isosceles triangle with perimeter 18 and one side of length 8 ?

A.6
B.12
C.14
D.16
E.18
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

2 KUDOS received
Target Test Prep Representative
User avatar
Status: Head GRE Instructor
Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 4

Kudos [?]: 117 [2] , given: 0

Re: GRE Math Challenge #34-the area of an isosceles triangle [#permalink] New post 03 Jan 2018, 07:19
2
This post received
KUDOS
Expert's post
sandy wrote:
Which of the folllowing could be the area of an isosceles triangle with perimeter 18 and one side of length 8 ?

A.6
B.12
C.14
D.16
E.18


Since the isosceles triangle has a perimeter of 18 and a side length of 8, we could have the following sides:

1) 8, 8, 2

or

2) 8, 5, 5

In option 1, the base is 2 and the legs (the sides that have equal length) are 8 each. The height of this triangle, h, satisfies the Pythagorean theorem in the form (b/2)^2 + h^2 = l^2 where b is the base and l is a leg of the isosceles triangle. Thus:

(2/2)^2 + h^2 = 8^2

1 + h^2 = 64

h^2 = 63

h = √63

Recall that the area of a triangle is (b x h)/2, so the area of the triangle is (2 x √63)/2 = √63. However, this is not one of the answer choices. Thus, we must consider option 2.

In option 2, the base is 8 and the legs are 5 each. So, we have:

(b/2)^2 + h^2 = l^2

(8/2)^2 + h^2 = 5^2

16 + h^2 = 25

h^2 = 9

h = √9 = 3

So, the area of the triangle is (8 x 3)/2 = 24/2 = 12.

Answer: B
_________________

Jeffery Miller
Head of GRE Instruction

GRE Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: GRE Math Challenge #34-the area of an isosceles triangle   [#permalink] 03 Jan 2018, 07:19
Display posts from previous: Sort by

GRE Math Challenge #34-the area of an isosceles triangle

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.