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

 It is currently 06 Jul 2020, 13:46

### 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

# Which of the following could be the area of an isosceles triangle with

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65014
Which of the following could be the area of an isosceles triangle with  [#permalink]

### Show Tags

01 Sep 2017, 00:01
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:47) correct 27% (02:26) wrong based on 84 sessions

### HideShow timer Statistics

Which of the following 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

_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3249
Location: India
GPA: 3.12
Which of the following could be the area of an isosceles triangle with  [#permalink]

### Show Tags

01 Sep 2017, 00:10
1
Bunuel wrote:
Which of the following 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

If the triangle is isosceles, 2 sides are have equal lengths
We know that the perimeter of the triangle is 18,
2x + y = 18
where x is the length of the 2 sides with equal lengths
and y is the length of the other side

Now, we know that one of the sides is 8

There are two possibilities, when x = 8 or y =8
If x = 8, the three sides are 8,8,2
The area calculated by Heron's formula is not part of the list of the answer options

If y = 8, the three sides are 5,5,8
The area is $$2*\frac{1}{2}*4*3$$ as it will form 2 right triangles with sides 3,4,5
Therefore, the area must be 12(Option B)
_________________
You've got what it takes, but it will take everything you've got
Intern
Joined: 20 Dec 2016
Posts: 10
Which of the following could be the area of an isosceles triangle with  [#permalink]

### Show Tags

01 Sep 2017, 00:19
pushpitkc wrote:
Bunuel wrote:
Which of the following 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

If the triangle is isosceles, 2 sides are have equal lengths
We know that the perimeter of the triangle is 18,
2x + y = 18
where x is the length of the 2 sides with equal lengths
and y is the length of the other side

Now, we know that one of the sides is 8

There are two possibilities, when x = 8 or y =8
If x = 8, the three sides are 8,8,2 which is not possible(does not obey the properties of triangles)
If y = 8, the three sides are 5,5,8

The area is $$2*\frac{1}{2}*4*3$$ as it will form 2 right triangles with sides 3,4,5
Therefore, the area must be 12(Option B)

Can u explain y 8,8,2 is not a valid triangle

Sent from my A0001 using GMAT Club Forum mobile app
Intern
Joined: 26 Aug 2017
Posts: 6
Re: Which of the following could be the area of an isosceles triangle with  [#permalink]

### Show Tags

01 Sep 2017, 00:31
Area of useless triangle is = a/4 x underroot of 4b2-a2 so it's and will be 12

Sent from my Redmi 4A using GMAT Club Forum mobile app
Manager
Joined: 08 Oct 2015
Posts: 217
Which of the following could be the area of an isosceles triangle with  [#permalink]

### Show Tags

Updated on: 01 Sep 2017, 00:50
pushpitkc wrote:
Bunuel wrote:
Which of the following 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

If the triangle is isosceles, 2 sides are have equal lengths
We know that the perimeter of the triangle is 18,
2x + y = 18
where x is the length of the 2 sides with equal lengths
and y is the length of the other side

Now, we know that one of the sides is 8

There are two possibilities, when x = 8 or y =8
If x = 8, the three sides are 8,8,2 which is not possible(does not obey the properties of triangles)
If y = 8, the three sides are 5,5,8

The area is $$2*\frac{1}{2}*4*3$$ as it will form 2 right triangles with sides 3,4,5
Therefore, the area must be 12(Option B)

8,8, and 2 is a possible isosceles triangle of area ~8.
8-8=0 <2 , 8-2= 6 <8 , 8+8= 16> 2, 8+2=10>8.

it follows all required rules

Originally posted by rahulkashyap on 01 Sep 2017, 00:44.
Last edited by rahulkashyap on 01 Sep 2017, 00:50, edited 1 time in total.
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3249
Location: India
GPA: 3.12
Re: Which of the following could be the area of an isosceles triangle with  [#permalink]

### Show Tags

01 Sep 2017, 00:49
Makesh617 wrote:
pushpitkc wrote:
Bunuel wrote:
Which of the following 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

If the triangle is isosceles, 2 sides are have equal lengths
We know that the perimeter of the triangle is 18,
2x + y = 18
where x is the length of the 2 sides with equal lengths
and y is the length of the other side

Now, we know that one of the sides is 8

There are two possibilities, when x = 8 or y =8
If x = 8, the three sides are 8,8,2 which is not possible(does not obey the properties of triangles)
If y = 8, the three sides are 5,5,8

The area is $$2*\frac{1}{2}*4*3$$ as it will form 2 right triangles with sides 3,4,5
Therefore, the area must be 12(Option B)

Can u explain y 8,8,2 is not a valid triangle

Sent from my A0001 using GMAT Club Forum mobile app

Hi Makesh617,

The area of a triangle with sides 8,8,2 is less than 8 and that is not an answer option
_________________
You've got what it takes, but it will take everything you've got
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11042
Location: United States (CA)
Re: Which of the following could be the area of an isosceles triangle with  [#permalink]

### Show Tags

07 Sep 2017, 06:13
Bunuel wrote:
Which of the following 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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
225 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Non-Human User
Joined: 09 Sep 2013
Posts: 15384
Re: Which of the following could be the area of an isosceles triangle with  [#permalink]

### Show Tags

29 Mar 2020, 05:17
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: Which of the following could be the area of an isosceles triangle with   [#permalink] 29 Mar 2020, 05:17
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6512868404388428, "perplexity": 1422.236919187931}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655890181.37/warc/CC-MAIN-20200706191400-20200706221400-00250.warc.gz"}