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# What is the area of right triangle ABC?

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Manager
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What is the area of right triangle ABC?  [#permalink]

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Updated on: 26 Aug 2017, 10:47
1
Data Sufficiency Geometry:

What is the area of right triangle ABC?

I) AB is 6
II) BC is 8

My first question is can we assume that B is the right angle in triangle ABC since B is written in between AB? If yes, the answer is C, or else E since multiple solutions can be found? Please let me know the answer too, thanks in advance.

OA: Not available.

Originally posted by aashishagarwal2 on 23 Aug 2017, 08:24.
Last edited by aashishagarwal2 on 26 Aug 2017, 10:47, edited 4 times in total.
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Re: What is the area of right triangle ABC?  [#permalink]

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23 Aug 2017, 08:39
1
Hii aashishagarwal2,
No you can not assume that B is 90° just because it is placed in between A and C. Problem must state that ABC is a right angled triangle at B or state that AC is a hypotenuse.

kudos if it helps.
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Re: What is the area of right triangle ABC?  [#permalink]

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23 Aug 2017, 08:49
Hii aashishagarwal2,
No you can not assume that B is 90° just because it is placed in between A and C. Problem must state that ABC is a right angled triangle at B or state that AC is a hypotenuse.

kudos if it helps.

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Re: What is the area of right triangle ABC?  [#permalink]

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23 Aug 2017, 09:46
2
aashishagarwal2
Hii,
In this case it seems that third side of triangle can take multiple values.
for further explanation see this https://www.youtube.com/watch?v=icUHqgCyKfc
so we can not find unique area of a triangle. So Answer must be E.
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Re: What is the area of right triangle ABC?  [#permalink]

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23 Aug 2017, 11:01
aashishagarwal2
Hii,
In this case it seems that third side of triangle can take multiple values.
for further explanation see this https://www.youtube.com/watch?v=icUHqgCyKfc
so we can not find unique area of a triangle. So Answer must be E.

Can you please re-read the entire question and confirm? Its stated as right triangle ABC and not triangle ABC. Can we now assume B is the right angle? Sorry for trouble.
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Re: What is the area of right triangle ABC?  [#permalink]

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23 Aug 2017, 11:08
Hii aashishagarwal2,

Even if ABC is right angled triangle there are two scenarios:
Scenario 1) hypotenuse is 8 then the remaining sides will be 6 and 2√7
Scenario 2) If 8 and 6 are two other sides of a right angled triangle then hypotenuse will be 10.

I hope, it is clear
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Re: What is the area of right triangle ABC?  [#permalink]

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23 Aug 2017, 22:44
1
We can not simply assume that the right angle is B.
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Re: What is the area of right triangle ABC?  [#permalink]

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23 Aug 2017, 23:00
1
It is clear that the statements alone are not sufficient to find the answer so (A), (B) and (D) are out.

We are left with (C) or (E)

Now lets consider two scenarios :

1. Triangle ABC is right angled at C
2. Triangle ABC is right angled at B

(Triangle ABC cannot be right angled at A because 6 will be the hypotenuse, which is not possible)

If we consider both statements together, two different areas are possible. (1/2 x 6 x 8 OR 1/2 x 6 x ~5.2) => No unique answer.

Hence, the answer should be (E)
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Re: What is the area of right triangle ABC?  [#permalink]

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24 Aug 2017, 00:00
2
aashishagarwal2 wrote:
Data Sufficiency Geometry:

What is the area of right triangle ABC?

I) AB is 6
II) BC is 8

My first question is can we assume that B is the right angle in triangle ABC since B is written in between AB? If yes, the answer is C, or else E since multiple solutions can be found? Please let me know the answer too, thanks in advance.

If it's given that triangle ABC is right you CANNOT assume that B is a right angle, it might as well be A or C. So, the answer to this question is E.

Could you please tell me the source of the question and exact form of it as it appears in the source? Thank you.
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Re: What is the area of right triangle ABC?  [#permalink]

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26 Aug 2017, 09:56
Hi brunel
Please correct me If I am wrong.
the question says ABC is a right angle triangle.So any of the points A, B, C will have 90 degree.

I) AB is 6 Not sufficient
II) BC is 8 Not sufficient

But when we combine 1 and 2. there will be only one possible triplet 6,8,10 will form a triangle .And neither Ab or BC will be hypotenuse.

So we can use AB and Bc to calculate the area using 1/2 *AB*BC=1/2*6*8=24

Thanks
Abhinash
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Re: What is the area of right triangle ABC?  [#permalink]

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26 Aug 2017, 10:05
abhinashgc wrote:
Hi brunel
Please correct me If I am wrong.
the question says ABC is a right angle triangle.So any of the points A, B, C will have 90 degree.

I) AB is 6 Not sufficient
II) BC is 8 Not sufficient

But when we combine 1 and 2. there will be only one possible triplet 6,8,10 will form a triangle .And neither Ab or BC will be hypotenuse.

So we can use AB and Bc to calculate the area using 1/2 *AB*BC=1/2*6*8=24

Thanks
Abhinash

Hii Abhinash,
but we do not know about hypotenuse.
what if BC is a hypotenuse. then the remaining 2 sides will be 6 and 2√7 . And area of a triangle will be different.
Hence E.
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Re: What is the area of right triangle ABC?  [#permalink]

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26 Aug 2017, 10:12
abhinashgc wrote:
Hi brunel
Please correct me If I am wrong.
the question says ABC is a right angle triangle.So any of the points A, B, C will have 90 degree.

I) AB is 6 Not sufficient
II) BC is 8 Not sufficient

But when we combine 1 and 2. there will be only one possible triplet 6,8,10 will form a triangle .And neither Ab or BC will be hypotenuse.

So we can use AB and Bc to calculate the area using 1/2 *AB*BC=1/2*6*8=24

Thanks
Abhinash

Hii Abhinash,
but we do not know about hypotenuse.
what if BC is a hypotenuse. then the remaining 2 sides will be 6 and 2√7 . And area of a triangle will be different.
Hence E.

Ok. So please assume BC is hypotenuse.Hypotenous^2= sum of other two side ^2.

Can it be true that BC^2=Ac^2+Ab^2 which means in this case 8^2=10^2+6^??Which is not.
This will be same if we assume Ab as hypotenuse. Hope its clear
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Re: What is the area of right triangle ABC?  [#permalink]

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26 Aug 2017, 10:19
abhinashgc wrote:
abhinashgc wrote:
Hi brunel
Please correct me If I am wrong.
the question says ABC is a right angle triangle.So any of the points A, B, C will have 90 degree.

I) AB is 6 Not sufficient
II) BC is 8 Not sufficient

But when we combine 1 and 2. there will be only one possible triplet 6,8,10 will form a triangle .And neither Ab or BC will be hypotenuse.

So we can use AB and Bc to calculate the area using 1/2 *AB*BC=1/2*6*8=24

Thanks
Abhinash

Hii Abhinash,
but we do not know about hypotenuse.
what if BC is a hypotenuse. then the remaining 2 sides will be 6 and 2√7 . And area of a triangle will be different.
Hence E.

Ok. So please assume BC is hypotenuse.Hypotenous^2= sum of other two side ^2.

Can it be true that BC^2=Ac^2+Ab^2 which means in this case 8^2=10^2+6^??Which is not.
This will be same if we assume Ab as hypotenuse. Hope its clear

see the solution given in image
Attachments

abc.jpg [ 592.17 KiB | Viewed 1520 times ]

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Re: What is the area of right triangle ABC?  [#permalink]

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26 Aug 2017, 10:25
Thanks a lot pushkarajnjadhav. I thought of only 6,8 and 10.Now its clear to me.
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What is the area of right triangle ABC?  [#permalink]

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26 Aug 2017, 10:46
Bunuel wrote:
aashishagarwal2 wrote:
Data Sufficiency Geometry:

What is the area of right triangle ABC?

I) AB is 6
II) BC is 8

My first question is can we assume that B is the right angle in triangle ABC since B is written in between AB? If yes, the answer is C, or else E since multiple solutions can be found? Please let me know the answer too, thanks in advance.

If it's given that triangle ABC is right you CANNOT assume that B is a right angle, it might as well be A or C. So, the answer to this question is E.

Could you please tell me the source of the question and exact form of it as it appears in the source? Thank you.

Hi Bunuel,

The source is Mitul Gada's class handout. Also, the exact words are as stated in the question "What is the area of right triangle ABC?". Since, they are saying right triangle ABC, I was hoping to assume B is the right angle. But guess you're saying we can't do that?
What is the area of right triangle ABC?   [#permalink] 26 Aug 2017, 10:46
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