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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # In triangle ABC,AB = AC= 2. Which of the following could be  Question banks Downloads My Bookmarks Reviews Important topics
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TAGS: Founder  Joined: 18 Apr 2015
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In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
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Expert's post 00:00

Question Stats: 41% (01:00) correct 58% (01:39) wrong based on 112 sessions

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
[Reveal] Spoiler: OA

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Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
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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!
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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? Founder  Joined: 18 Apr 2015
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Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
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Expert's post

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
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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. Founder  Joined: 18 Apr 2015
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Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
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Expert's post
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 _________________

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Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
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Carcass wrote:

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.
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Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
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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.

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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.
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Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
Carcass wrote:

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
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Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
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
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Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
Expert's post

Regards
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Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
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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.
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Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
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 Moderator Joined: 16 Sep 2019
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Re: In triangle ABC,AB = AC= 2. Which of the following could be [#permalink]
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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 [ 3.4 KiB | Viewed 148 times ]

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If you like my solution, do give kudos! Re: In triangle ABC,AB = AC= 2. Which of the following could be   [#permalink] 01 Jul 2020, 10:33
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