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

 It is currently 27 Jan 2020, 16:09

### 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 sides of a triangle are a, b, and c. Are the three angles all less

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60687
The sides of a triangle are a, b, and c. Are the three angles all less  [#permalink]

### Show Tags

06 Nov 2019, 02:29
00:00

Difficulty:

75% (hard)

Question Stats:

41% (02:24) correct 59% (02:20) wrong based on 32 sessions

### HideShow timer Statistics

The sides of a triangle are a, b, and c. Are the three angles all less than 90 measure degrees?

(1) The areas of the semi-circles with the radius a, b, c are 4, 5, 6, respectively.

(2) $$c < a + b < c + 2$$

Are You Up For the Challenge: 700 Level Questions

_________________
VP
Joined: 19 Oct 2018
Posts: 1296
Location: India
Re: The sides of a triangle are a, b, and c. Are the three angles all less  [#permalink]

### Show Tags

06 Nov 2019, 05:46
Statement 1

We know the areas of triangle; hence, we can find the radius of the circles.
We know all the sides of the triangle; we can calculate all the angles using cosine formula or we can check whether all the angles are acute or not using pythagorean inequality.

Sufficient

Statement 2-

a+b<c+2

1. if a=1.4; b=1.4; and c=1.4 (it's an equilateral triangle)

2. if a=0.6; b=0.6; and c=0.9 (it's an obtuse angle triangle)
(0.6)^2+(0.6)^2<(0.9)^2
0.72<0.81

Insufficient

Bunuel wrote:
The sides of a triangle are a, b, and c. Are the three angles all less than 90 measure degrees?

(1) The areas of the semi-circles with the radius a, b, c are 4, 5, 6, respectively.

(2) $$c < a + b < c + 2$$

Are You Up For the Challenge: 700 Level Questions
Manager
Joined: 10 Jun 2019
Posts: 119
Re: The sides of a triangle are a, b, and c. Are the three angles all less  [#permalink]

### Show Tags

20 Nov 2019, 04:34
Statement 1 : From the area of the semi circles we can find the sides.The triangle will have a unique set of sides and hence a unique set of angles .From the angles we will be able to tell if the triangle is acute or isn't.
OR
Once we have the sides, we will perform the acute angle test: that is for all the angles of the triangle to be acute(<90) , the sum of the squares of any two sides MUST be greater than the square of the last side. That is, a^2 +b^2>c^2 and c^2 +b^2>b^2 and a^2 +c^2>b^2 .However, since c is the largest side, we only to need to do it for a^2 +b^2>c^2 .After all, the largest side is opposite the largest angle and if it happens to be acute,the other angles must also be acute

SUFFICIENT

Statement 2 :
If the sides are either 1/1/1( equilateral triangle)or if the sides are 1/1/1.414 (right angled isosceles) the statement holds true.
INSUFFICIENT

Re: The sides of a triangle are a, b, and c. Are the three angles all less   [#permalink] 20 Nov 2019, 04:34
Display posts from previous: Sort by

# The sides of a triangle are a, b, and c. Are the three angles all less

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne