Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 06 May 2015, 11:55

### 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

# An obtuse triangle is a triangle that has an interior angle

Author Message
TAGS:
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1269
Followers: 23

Kudos [?]: 158 [0], given: 0

An obtuse triangle is a triangle that has an interior angle [#permalink]  24 Jul 2006, 05:34
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
An obtuse triangle is a triangle that has an interior angle whose measure is greater than 90 degrees. John has drawn all obtuse triangles with an area of 20 square inches whose angle measures in degrees are all multiples of 10. How many triangles has he drawn?

(A) 13 (B) 14 (C) 15 (D) 16 (E) more than 16
SVP
Joined: 24 Sep 2005
Posts: 1893
Followers: 11

Kudos [?]: 139 [0], given: 0

kevincan wrote:
An obtuse triangle is a triangle that has an interior angle whose measure is greater than 90 degrees. John has drawn all obtuse triangles with an area of 20 square inches whose angle measures in degrees are all multiples of 10. How many triangles has he drawn?

(A) 13 (B) 14 (C) 15 (D) 16 (E) more than 16

First of all, i think the data of the area is a distraction since with any 3 fixed angle measures, we can adjust the sides to get the required area.
Since one angle ( the obstute one) can be 100,110,120.....170 ( 180 is not counted coz the triangle will become a line then)
+ angle is 100, we have the other two angles be (10,70) , (20,60 ) , (30,50), (40,40) ..the order is not important here.
+ 110: ( 10,60) , (20,50), (30,40)
+ 120: (10,50) , (20,40), (30,30)
+130: ( 10,40) , (20,30)
+140: (10,30), (20,20)
+150: (10,20)
+160: (10,10)
170: such triangle does not exist.

==> we have 16 such triangles
Senior Manager
Joined: 22 May 2006
Posts: 375
Location: Rancho Palos Verdes
Followers: 1

Kudos [?]: 28 [0], given: 0

We don't need to consider area here, 'cuz we can draw to match the area of triangle with given interior angles.

180=10(a+b+c)
18 = a+b+c (where a,b,c are integers)
let c>9

if c=10
a+b = 8
a can be 1,2,3,4,(5,6,7) (redundancies)
4 possible outcomes.
if c=11
a+b = 7
a can be 1,2,3,(4,5,6)
3 possible outcomes.
if c=12
a+b = 6
a can be 1,2,3,(4,5)
3 possible outcomes
.....
Total possible outcomes = (4+3+3+2+2+1+1) = 16

Thus, D must be it.
_________________

The only thing that matters is what you believe.

Manager
Joined: 01 Jun 2006
Posts: 82
Followers: 1

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

I think E. You can have infinite combinations.

Area = 1/2 * base * Height.

You can vary the base and height to get any number of triangles. The obtuse information is just a distraction from the real problem.
Manager
Joined: 26 Jun 2006
Posts: 152
Followers: 1

Kudos [?]: 1 [0], given: 0

Got 16 too. (Assuming we don't consider a triangle with 180,0,0 angles as a trinagle.)
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1269
Followers: 23

Kudos [?]: 158 [0], given: 0

laxieqv wrote:
kevincan wrote:
An obtuse triangle is a triangle that has an interior angle whose measure is greater than 90 degrees. John has drawn all obtuse triangles with an area of 20 square inches whose angle measures in degrees are all multiples of 10. How many triangles has he drawn?

(A) 13 (B) 14 (C) 15 (D) 16 (E) more than 16

First of all, i think the data of the area is a distraction since with any 3 fixed angle measures, we can adjust the sides to get the required area.
Since one angle ( the obstute one) can be 100,110,120.....170 ( 180 is not counted coz the triangle will become a line then)
+ angle is 100, we have the other two angles be (10,70) , (20,60 ) , (30,50), (40,40) ..the order is not important here.
+ 110: ( 10,60) , (20,50), (30,40)
+ 120: (10,50) , (20,40), (30,30)
+130: ( 10,40) , (20,30)
+140: (10,30), (20,20)
+150: (10,20)
+160: (10,10)
170: such triangle does not exist.

==> we have 16 such triangles

Great! the area wasn't a distraction. A better wording would be "no triangle is similar to any other" I 'm glad nearly everybody caught it.
SVP
Joined: 30 Mar 2006
Posts: 1739
Followers: 1

Kudos [?]: 46 [0], given: 0

D 16 triangles

With obtuse angle 100 - 4 traingles (70,10) (60,20) (50,30) (40,40)
With obtuse angle 110 - 3 triangles
With obtuse angle 120 - 3 triangles
With obtuse angle 130 - 2 triangles
With obtuse angle 140 - 2 triangles
With obtuse angle 150 - 1 triangle
With obtuse angle 160 - 1 triangle
With obtuse angle 170 - 0
Total = 16
Similar topics Replies Last post
Similar
Topics:
7 What is the area of an obtuse angled triangle whose two side 10 09 Jul 2012, 20:43
9 Consider an obtuse-angled triangles with sides 8 cm, 15 cm a 8 04 Oct 2011, 07:33
4 Area of triangle, given ratio of interior angles 5 01 Nov 2009, 03:06
3 What is the area of an obtuse angled triangle whose two 12 03 Mar 2008, 09:42
An obtuse triangle is a triangle that has an interior angle 9 26 Jul 2006, 12:26
Display posts from previous: Sort by