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If the area of triangular region RST is 25, what is the

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If the area of triangular region RST is 25, what is the [#permalink] New post 21 May 2008, 01:53
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A
B
C
D
E

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If the area of triangular region RST is 25, what is the perimeter of RST?

(1) The length of one side of RST is 5\sqrt{2}.
(2) RST is a right isosceles triangle.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 25 Oct 2013, 06:45, edited 1 time in total.
Edited the question and added the OA
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Re: DS2-24 [#permalink] New post 21 May 2008, 02:21
prasannar wrote:
24. If the area of triangular region RST is 25, what is the perimeter of RST?
(1) The length of one side of RST is 5 sqrt 2.
(2) RST is a right isosceles triangle.

Plz explain


B

1/2*a^2 = 25 --> a =?
then b =a*sqare root(2)

and perimeter = b+ 2a, suff
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Re: DS2-24 [#permalink] New post 21 May 2008, 02:30
(1) The length of one side is given . but no information abt other sides. Insufficient
(2)The triangle is right isosceles let one side be x So area=1/2 *base*height=25.
here base=height (isoscels triagle)=x
Therefore, 1/2 *x*x=25 so x can be found
since right triangle so third side can be found say y
Perimeter is 2x+y
So sufficient
Hence answer is B
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Re: DS2-24 [#permalink] New post 21 May 2008, 02:47
The question stem tells us that 1/2 * b * h = 25 and asks us to determine what RS + ST + TR is.

(1) Statement just tells us what one of the 3 sides is where the b and h could still take several values and affect the other two sides:

Insufficient

(2) This statement simply tells us that b = h so b^2 = 50. If we know the lengths of two sides of a right triangle, then we can determine (I won't calculate it here since it would be a waste of time on test day) the length of the other. So:

Sufficient

Answer = [B]
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Re: DS2-24 [#permalink] New post 21 May 2008, 05:47
I think C is right..how do we know from B which side is base?

i mean i could have a 90-degree-45-45 isso triangle and it will have perimeter of 10+5+5=20..

i could have a different isso triangle..
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Re: DS2-24 [#permalink] New post 21 May 2008, 13:05
i dont get it ... from B, you know that base=height=5*root(2) .... and since its a right isoceles, the hypotenuse will be 10 ... wont it ?
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Re: DS2-24 [#permalink] New post 21 May 2008, 13:46
pmenon wrote:
i dont get it ... from B, you know that base=height=5*root(2) .... and since its a right isoceles, the hypotenuse will be 10 ... wont it ?



no it wont..just draw a 3-4-5 right angle tirangle or a 5-12-13 right angle,triangle..
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Re: DS2-24 [#permalink] New post 21 May 2008, 14:28
but a 3-4-5 isnt an isoceles triangle ... or am i missing something ?
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Re: DS2-24 [#permalink] New post 21 May 2008, 14:39
fresinha12 wrote:
pmenon wrote:
i dont get it ... from B, you know that base=height=5*root(2) .... and since its a right isoceles, the hypotenuse will be 10 ... wont it ?



no it wont..just draw a 3-4-5 right angle tirangle or a 5-12-13 right angle,triangle..


Doesn't a right isosceles triangle means that the two equal sides make up the right angle?
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Re: DS2-24 [#permalink] New post 21 May 2008, 19:31
the answer should be B since in a right isosceles triangle, base = height and area is (base*height)/2 - so we can get both the sides and then hypotenuse is side*sqrt 2 - so I am a bit surprised that the answer is C - it is anyway not A and D. E is also out of the question.
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Re: DS2-24 [#permalink] New post 21 May 2008, 20:47
fresinha12 wrote:
I think C is right..how do we know from B which side is base?

i mean i could have a 90-degree-45-45 isso triangle and it will have perimeter of 10+5+5=20..

i could have a different isso triangle..


hi fresinha12,
is it required to know whats the base???
in any case let what ever be the base the area will be same
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Re: DS2-24 [#permalink] New post 25 Oct 2013, 05:40
rohit929 wrote:
fresinha12 wrote:
I think C is right..how do we know from B which side is base?

i mean i could have a 90-degree-45-45 isso triangle and it will have perimeter of 10+5+5=20..

i could have a different isso triangle..


hi fresinha12,
is it required to know whats the base???
in any case let what ever be the base the area will be same


I agree with Rohit, you can change the position but the relative sides will be the same hence you can trace a perpendicular for the height wherever you want and you would still have the same area and same perimeter.

Hence for me (B) is the correct choce
Let us know if this is the OA will you?
Thanks
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Re: DS2-24 [#permalink] New post 25 Oct 2013, 06:51
Expert's post
jlgdr wrote:
rohit929 wrote:
fresinha12 wrote:
If the area of triangular region RST is 25, what is the perimeter of RST?

(1) The length of one side of RST is 5\sqrt{2}.
(2) RST is a right isosceles triangle.

I think C is right..how do we know from B which side is base?

i mean i could have a 90-degree-45-45 isso triangle and it will have perimeter of 10+5+5=20..

i could have a different isso triangle..


hi fresinha12,
is it required to know whats the base???
in any case let what ever be the base the area will be same


I agree with Rohit, you can change the position but the relative sides will be the same hence you can trace a perpendicular for the height wherever you want and you would still have the same area and same perimeter.

Hence for me (B) is the correct choce
Let us know if this is the OA will you?
Thanks
Cheers
J :)


The correct answer is B. From (2) we know that 1/2*leg^2=25 --> we can get the length of the legs, and since it's a 45-45-90 right isosceles triangle, we can get the length of the hypotenuse too.
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Re: If the area of triangular region RST is 25, what is the [#permalink] New post 07 Dec 2013, 10:57
I don't understand why (1) is not sufficient. Doesn't (1) imply that the triangle is an isosceles right triangle since the height = 5*sqrt(2)?
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Re: If the area of triangular region RST is 25, what is the [#permalink] New post 08 Dec 2013, 06:03
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TooLong150 wrote:
I don't understand why (1) is not sufficient. Doesn't (1) imply that the triangle is an isosceles right triangle since the height = 5*sqrt(2)?


No. Any triangle with the base (side) of 5\sqrt{2} and height of \frac{10}{\sqrt{2}} would have the area of 25.
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Re: If the area of triangular region RST is 25, what is the   [#permalink] 08 Dec 2013, 06:03
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