Last visit was: 17 Jun 2024, 19:36 It is currently 17 Jun 2024, 19:36

Close

GRE Prep 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 GRE 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.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 28946
Own Kudos [?]: 33721 [13]
Given Kudos: 25365
Send PM
Most Helpful Expert Reply
Verbal Expert
Joined: 18 Apr 2015
Posts: 28946
Own Kudos [?]: 33721 [5]
Given Kudos: 25365
Send PM
Most Helpful Community Reply
avatar
Director
Director
Joined: 03 Sep 2017
Posts: 518
Own Kudos [?]: 680 [7]
Given Kudos: 0
Send PM
General Discussion
avatar
Intern
Intern
Joined: 06 Nov 2017
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
IlCreatore wrote:
This kind of question has to be answered using the range of areas a triangle can have given two sides.

The smallest triangle is the one with area slightly higher than 0 when the third side is so small that the triangle is shrank towards its base.

The largest triangle is the right triangle with legs equal to the two given sides, in this case 2 and 2.

Thus, the area range is \(0<Area\leq \frac{2*2}{2}\) or \(0<area\leq 2\).

The answers are A, B, C, D!



Does the right triangle has the greatest area?? Can't the included angle be obtuse which would result in a larger area?
avatar
Manager
Manager
Joined: 15 Feb 2018
Posts: 53
Own Kudos [?]: 34 [0]
Given Kudos: 0
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
I am so incapable of understanding this question and also the solutions above. It is not necessarily a 45-45-90 triangle so isn't there many possibilities?

Would it be possible to give me a detailed explanation of the solution in the problem? I have this "it cannot be determined" answer in mind but obviously I am wrong.

The height or the base of the triangle can be anything, no? Would have been easier to explain what I am thinking with pictures but I guess they're not allowed.
Verbal Expert
Joined: 18 Apr 2015
Posts: 28946
Own Kudos [?]: 33721 [2]
Given Kudos: 25365
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
2
Expert Reply
Quote:
From the properties of triangles, we do know that the third side must be between the sum of the two sides: 2+2=4, the longest side must be 3.9,3.8 and so on, AND the difference of the same two side: 2-2=0, which means that the third side must be 0.1,0.2, 0.3 and so forth.

Therefore, the area of the triangle must be between 0 and 2.


More simple than this is very difficult to figure it out how to explain :(
User avatar
Manager
Manager
Joined: 26 Jun 2017
Posts: 102
Own Kudos [?]: 69 [2]
Given Kudos: 0
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
2
Carcass wrote:
Here, your assumption about the angle is wrong.

We do know from the stem that the triangle is a right triangle, with two equal sides 2 and 2, which means that we do also have two angles of 45° and the other of 90° that is on the opposite of the longest side: the hypotenus

From the properties of triangles, we do know that the third side must be between the sum of the two sides: 2+2=4, the longest side must be 3.9,3.8 and so on, AND the difference of the same two side: 2-2=0, which means that the third side must be 0.1,0.2, 0.3 and so forth.

Therefore, the area of the triangle must be between 0 and 2.

Hope this helps.

REGARDS

But, on what basis can you regard this triangle as a right triangle, you can surely say it as isosceles, and only after drawing a perpendicular to the base, you can say that this is a right triangle.
avatar
Manager
Manager
Joined: 26 Jan 2018
Posts: 189
Own Kudos [?]: 166 [0]
Given Kudos: 0
GRE 1: Q165 V156
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
2
From question it is an isosceles triangle.

For area to be highest, it has to be a right angled triangle.

1/2 * base *height

1/2 * 2 * 2 = 2 is highest possible area. Any option less than this can be answer option.

Hence all the 4 option.

Please correct if my answer is wrong.
avatar
Intern
Intern
Joined: 27 Nov 2014
Posts: 30
Own Kudos [?]: 8 [0]
Given Kudos: 0
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
Basic, the more uniform the shape is the higher the area will be. For a triangle with two equal sides the right triangle with 45: 45: 90 got the highest area.
avatar
Intern
Intern
Joined: 13 Oct 2018
Posts: 21
Own Kudos [?]: 4 [0]
Given Kudos: 0
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
Carcass wrote:
Here, your assumption about the angle is wrong.

We do know from the stem that the triangle is a right triangle, with two equal sides 2 and 2, which means that we do also have two angles of 45° and the other of 90° that is on the opposite of the longest side: the hypotenus

From the properties of triangles, we do know that the third side must be between the sum of the two sides: 2+2=4, the longest side must be 3.9,3.8 and so on, AND the difference of the same two side: 2-2=0, which means that the third side must be 0.1,0.2, 0.3 and so forth.

Therefore, the area of the triangle must be between 0 and 2.

Hope this helps.

REGARDS

we know that the third side will be |2-2|<x<|2+2| i.e lie between 0-4. So my doubt arises that the area will be between 0 to 2.As the area is between 0-2 will the option D be the part of the answer ? I feel the areas will only be 0.5 1 and 1.5 the area can be 1.999 too but not 2 is what I feel. Please correct me if I'm wrong I have my gre in 4 days
Manager
Manager
Joined: 02 Sep 2019
Posts: 181
Own Kudos [?]: 143 [1]
Given Kudos: 94
Concentration: Finance
GRE 1: Q151 V148
GPA: 3.14
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
1
why we assume it is a right triangle?
The question never mention about the height and if they asking about something else they will put it for you.
yeah it can be an isosceles triangle with different angle, but if that was the case how are we going to calculate the area?

PLEASE IF I'M WRONG CORRECT ME THIS WILL HELP ME A LOT
Verbal Expert
Joined: 18 Apr 2015
Posts: 28946
Own Kudos [?]: 33721 [0]
Given Kudos: 25365
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
Expert Reply
See my explanation above, please.

Regards
User avatar
Senior Manager
Senior Manager
Joined: 10 Feb 2020
Posts: 496
Own Kudos [?]: 340 [3]
Given Kudos: 299
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
2
1
Bookmarks
Property of triangle:
Sum of 2 sides must be greater than 3rd side:
side1=2, side2=2
side1+side2 = 4
means third side must be less than 4

Another property of triangle:
Difference of 2 sides must be less than 3rd side
side1=2, side=2
side1-side2 = 2-2 =0
means third side must be greater than zero

The value will lie between 0 - 2.
avatar
Intern
Intern
Joined: 27 May 2020
Posts: 7
Own Kudos [?]: 7 [0]
Given Kudos: 0
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
Carcass wrote:

The last collection of questions for the GRE Quant - 2019



In triangle ABC,AB = AC= 2. Which of the following could be the area of the triangle ABC ?

Indicate all possible areas

❑ 0.5

❑ 1.0

❑ 1.5

❑ 2.0

❑ 2.5

❑ 3.0


I have no idea where im going wrong, please correct me.

so I draw a height from A to the base, call it h
call BC=b

we know that 0<b<4

so I took 2 extremes:

1) b=0.1

by Pythagoras, h= sqrt(2^2 - (0.1/2)^2) = 2

so minimum area is 0.09 (approx. equal to 0)

2) b=3.9

h = sqrt (2^2 - (3.9/2)^2) = 0.44

maximum area= 3.9*0.44/2= 0.9

I knowwww that something must be wrong can someone help out pleaseee
avatar
Retired Moderator
Joined: 16 Sep 2019
Posts: 187
Own Kudos [?]: 283 [2]
Given Kudos: 0
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
1
1
Bookmarks
There is a property that the right angled triangle has the largest area.
Now, we are given that two sides are equal. If two sides are equal then the angles opposite them will also be equal.
So we get a 45-45-90 right angled triangle.
Now, the base and perpendicular = 2.
So, the area = \(\frac{1}{2} \times 2 \times 2 = 2\)

2 is the largest area we can get.
Now, if the third side = 0, then essentially we get a line of length 2. and the area of triangle becomes 0.

So, the minimum area has to be greater than 0. and maximum area is 2.

The values of area possible lie between 0 and 2.

\(0 < Area < 2\)

OA, A,B,C,D
katerjigeorge wrote:
Carcass wrote:


In triangle ABC,AB = AC= 2. Which of the following could be the area of the triangle ABC ?

Indicate all possible areas

❑ 0.5

❑ 1.0

❑ 1.5

❑ 2.0

❑ 2.5

❑ 3.0


I have no idea where im going wrong, please correct me.

so I draw a height from A to the base, call it h
call BC=b

we know that 0<b<4

so I took 2 extremes:

1) b=0.1

by Pythagoras, h= sqrt(2^2 - (0.1/2)^2) = 2

so minimum area is 0.09 (approx. equal to 0)

2) b=3.9

h = sqrt (2^2 - (3.9/2)^2) = 0.44

maximum area= 3.9*0.44/2= 0.9

I knowwww that something must be wrong can someone help out pleaseee

Attachments

right triangle.png
right triangle.png [ 3.4 KiB | Viewed 9193 times ]

Intern
Intern
Joined: 11 Feb 2021
Posts: 7
Own Kudos [?]: 2 [0]
Given Kudos: 0
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
Farina wrote:
Property of triangle:
Sum of 2 sides must be greater than 3rd side:
side1=2, side2=2
side1+side2 = 4
means third side must be less than 4

Another property of triangle:
Difference of 2 sides must be less than 3rd side
side1=2, side=2
side1-side2 = 2-2 =0
means third side must be greater than zero

The value will lie between 0 - 2.




Hi, I understand everything above until you said that "the value will lie between 0-2". can you explain how you got that
Retired Moderator
Joined: 09 Jan 2021
Posts: 576
Own Kudos [?]: 839 [1]
Given Kudos: 194
GRE 1: Q167 V156
GPA: 4
WE:Analyst (Investment Banking)
Send PM
In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
1
gd2906 wrote:
Farina wrote:
Property of triangle:
Sum of 2 sides must be greater than 3rd side:
side1=2, side2=2
side1+side2 = 4
means third side must be less than 4

Another property of triangle:
Difference of 2 sides must be less than 3rd side
side1=2, side=2
side1-side2 = 2-2 =0
means third side must be greater than zero

The value will lie between 0 - 2.



Hi, I understand everything above until you said that "the value will lie between 0-2". can you explain how you got that


Hi!

The length of the 3rd side should be less than the sum of the other two sides and greater than the difference between the two sides
So, lets say AC is the third side.

2+2=4
2-2=0

Thus, 0<AC<4
Thus AC lies between 0 and 4. It could be any value, not necessarily integer value.

Hope this helps!
Senior Manager
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Own Kudos [?]: 155 [0]
Given Kudos: 81
Concentration: , International Business
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
Among all, Right Angle triangle has maximum area. Hence area can have maximum of 2*2/2 i.e 2. below this , all values are possible.
Intern
Intern
Joined: 05 Jan 2023
Posts: 22
Own Kudos [?]: 16 [1]
Given Kudos: 35
GRE 1: Q164 V160
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
1
The easiest way to understand this question is to draw out (or visualise) a right angle triangle with both sides AB and AC as the legs and the third side BC as the hypotenuse.

The area of the triangle in this scenario will be

(1/2)BH = (1/2)*2*2 = 2

If we imagine AB as the base and AC as the height, we can visualize the AC changing as the angle BAC widens or reduces.

This helps us to retain AB as the base and have a varied height.

In both cases with a widened angle BAC or reduced BAC, the height reduces and can reduce to almost zero as the angle BAC gets to either 0 degrees or 180 degrees.

Since it is a triangle, the area cannot be 0, the area is above 0 and less than or equal to 2.

Hence, 0 > Area >= 2

The answers A to D are in this range.
avatar
Intern
Intern
Joined: 04 Nov 2023
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
Why 2 is included in answer if answer lies between 0-2?
Prep Club for GRE Bot
[#permalink]
 1   2   
Moderators:
Moderator
1088 posts
GRE Instructor
218 posts

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