It is currently 17 Nov 2017, 20:20

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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: 42248

Kudos [?]: 132522 [0], given: 12324

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

Show Tags

01 Sep 2017, 01:01
Expert's post
2
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

59% (01:42) correct 41% (01:21) wrong based on 42 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
[Reveal] Spoiler: OA

_________________

Kudos [?]: 132522 [0], given: 12324

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 1594

Kudos [?]: 667 [0], given: 17

Location: India
WE: Sales (Retail)
Which of the following could be the area of an isosceles triangle with [#permalink]

Show Tags

01 Sep 2017, 01:10
1
This post was
BOOKMARKED
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)
_________________

Stay hungry, Stay foolish

Kudos [?]: 667 [0], given: 17

Intern
Joined: 20 Dec 2016
Posts: 10

Kudos [?]: 2 [0], given: 12

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

Show Tags

01 Sep 2017, 01:19
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

Kudos [?]: 2 [0], given: 12

Intern
Joined: 26 Aug 2017
Posts: 5

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

Re: Which of the following could be the area of an isosceles triangle with [#permalink]

Show Tags

01 Sep 2017, 01:31
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

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

Manager
Joined: 09 Oct 2015
Posts: 91

Kudos [?]: 3 [0], given: 9

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

Show Tags

01 Sep 2017, 01:44
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

Last edited by rahulkashyap on 01 Sep 2017, 01:50, edited 1 time in total.

Kudos [?]: 3 [0], given: 9

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 1594

Kudos [?]: 667 [0], given: 17

Location: India
WE: Sales (Retail)
Re: Which of the following could be the area of an isosceles triangle with [#permalink]

Show Tags

01 Sep 2017, 01:49
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
_________________

Stay hungry, Stay foolish

Kudos [?]: 667 [0], given: 17

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1806

Kudos [?]: 919 [0], given: 3

Location: United States (CA)
Re: Which of the following could be the area of an isosceles triangle with [#permalink]

Show Tags

07 Sep 2017, 07:13
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

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

Kudos [?]: 919 [0], given: 3

Re: Which of the following could be the area of an isosceles triangle with   [#permalink] 07 Sep 2017, 07:13
Display posts from previous: Sort by