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Director  Joined: 05 Jan 2008
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If the area of triangular region RST is 25, what is the  [#permalink]

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Project DS Butler: Day 54: Data Sufficiency (DS107)

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.

Originally posted by prasannar on 21 May 2008, 02:53.
Last edited by gmatbusters on 29 Dec 2018, 10:04, edited 2 times in total.
Edited the question and added the OA
VP  Joined: 04 May 2006
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Re: If the area of triangular region RST is 25, what is the  [#permalink]

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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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Director  Joined: 18 May 2008
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Re: If the area of triangular region RST is 25, what is the  [#permalink]

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(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
Intern  Joined: 07 May 2008
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Re: If the area of triangular region RST is 25, what is the  [#permalink]

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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

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Re: If the area of triangular region RST is 25, what is the  [#permalink]

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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: If the area of triangular region RST is 25, what is the  [#permalink]

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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: If the area of triangular region RST is 25, what is the  [#permalink]

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but a 3-4-5 isnt an isoceles triangle ... or am i missing something ?
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Re: If the area of triangular region RST is 25, what is the  [#permalink]

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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: If the area of triangular region RST is 25, what is the  [#permalink]

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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: If the area of triangular region RST is 25, what is the  [#permalink]

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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
Cheers
J Math Expert V
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Posts: 58422
Re: If the area of triangular region RST is 25, what is the  [#permalink]

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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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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]

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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]

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So the prompt tells us that the area of a triangle is 25 or that b*h=50
we are looking for the perimeter

(I) doesn't really tell us anything. Giving us one side is useless because we have no idea what the other sides could be
(II) actually tells us quite a lot. The fact that it is an isosceles right triangle tells us that b=h, so we know that those sides are rt(50) long and we can use that information to figure out the hypotenuse and add them up to get the perimeter.
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Re: If the area of triangular region RST is 25, what is the  [#permalink]

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B.
Statement 1- insufficient just says one side is 5 root 2 but no info about the other 2 sides is given
Statement 2- sufficient .. Isosceles right angled triangle therefore 1/2*side^2=25 side^2=50 side =root 50
Therefore hypotenuse = 2* (5 root 2) = 10
Perimeter =. 2(root 50) + 10
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Re: If the area of triangular region RST is 25, what is the  [#permalink]

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prasannar 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.

from the given information: bh=50
we can have 5, 10, 5*sqrt(2)
or we can have 5*sqrt(2), 5*sqrt(2), 10
1 alone not sufficient.

2. we know that b=h => b^2=50 -> b=5*sqrt(2). since it is a 45-45-90 triangle, we can find the value of the hypotenuse.
2 alone is sufficient.

B
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Re: If the area of triangular region RST is 25, what is the  [#permalink]

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Top Contributor
prasannar 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.

VERY IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in our free video: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1103

This technique can save a lot of time.

Target question: What is the perimeter of RST?

Given: The area of triangular region RST is 25.

Statement 1: The length of one of the sides is 5√2
There are several possible triangles such that the length of one side is 5√2. Here are two: Notice that the perimeter for each triangle is DIFFERENT. In other words, statement 1 does not lock our shape into having just one perimeter.
As such, statement 1 is NOT SUFFICIENT

Statement 2: The triangle is a right isosceles triangle
This fact alone forces the triangle into having a 90-degree angle, 2 equal angles and 2 equal sides. Of course there still many different triangles (with different perimeters) that meet these conditions: HOWEVER, it is given that the area of the triangle is 25. Among the infinite number of isosceles right triangles, ONLY ONE has an area of 25.
So, statement 2 (along with the given information) "locks" our triangle into ONE and ONLY ONE shape, which means there's only one possible perimeter.
As such, statement 2 is SUFFICIENT.
IMPORTANT: Need we actually find the perimeter of this triangle? No. We need only recognize that we COULD find the perimeter (if we so inclined to do so)

RELATED VIDEO

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Originally posted by GMATPrepNow on 29 Sep 2016, 08:25.
Last edited by GMATPrepNow on 16 Apr 2018, 12:46, edited 1 time in total.
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Re: If the area of triangular region RST is 25, what is the  [#permalink]

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Bunuel wrote:
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.

Bunuel egmat

It is stated in the question thread that we are dealing with a rst(right-side triangle), if i understand it right.

if the given triangle is indeed a right angle triangle, then :

statement1: one side =$$5\sqrt{2}$$. if the hypotenuse is this side, then the area can't be 25 as the other sides come out to be 5 & 5, so one of the other sides has to be this side.
we already know that b*h=50, so the second side is also equal to $$5\sqrt{2}$$. We can know find the hypotenuse (10) and thus the perimeter.

This, this option is sufficient.

Statement2: I agree that this statement is sufficient.

Thus the correct option should be C.

Let me know if i am missing something.
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Re: If the area of triangular region RST is 25, what is the  [#permalink]

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anurag564 wrote:
Bunuel wrote:
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.

Bunuel egmat

It is stated in the question thread that we are dealing with a rst(right-side triangle), if i understand it right.

if the given triangle is indeed a right angle triangle, then :

statement1: one side =$$5\sqrt{2}$$. if the hypotenuse is this side, then the area can't be 25 as the other sides come out to be 5 & 5, so one of the other sides has to be this side.
we already know that b*h=50, so the second side is also equal to $$5\sqrt{2}$$. We can know find the hypotenuse (10) and thus the perimeter.

This, this option is sufficient.

Statement2: I agree that this statement is sufficient.

Thus the correct option should be C.

Let me know if i am missing something.

Hi

1) In the main question (before the two statements), Nowhere is it stated that RST is a right angled triangle. It just means that the three vertices of this triangle are named as R, S, T respectively. RST doesn't mean right-side triangle, there is no such official term as 'right side triangle'. So we cannot assume it to be a right angled triangle.

2) When each statement alone is sufficient to answer a question in GMAT, then the answer to be marked is D, not C. (but of course here answer is neither C nor D, its B).
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Re: If the area of triangular region RST is 25, what is the  [#permalink]

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anurag564 wrote:
Bunuel wrote:
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.

Bunuel egmat

It is stated in the question thread that we are dealing with a rst(right-side triangle), if i understand it right.

if the given triangle is indeed a right angle triangle, then :

statement1: one side =$$5\sqrt{2}$$. if the hypotenuse is this side, then the area can't be 25 as the other sides come out to be 5 & 5, so one of the other sides has to be this side.
we already know that b*h=50, so the second side is also equal to $$5\sqrt{2}$$. We can know find the hypotenuse (10) and thus the perimeter.

This, this option is sufficient.

Statement2: I agree that this statement is sufficient.

Thus the correct option should be C.

Let me know if i am missing something.

First of all, if you claim that each statement is sufficient, then the answer should be D, not C. Next, when considering (1) alone, we don't know whether the triangle is right angled nor that it's isosceles. All we know is the area and the lengths of one side, which is not enough to get other two sides.

Hope it's clear.
_________________ Re: If the area of triangular region RST is 25, what is the   [#permalink] 19 Jan 2018, 07:42

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