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# If the area of traingleular region RST is 25, what is the

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Manager
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If the area of traingleular region RST is 25, what is the [#permalink]  30 Oct 2007, 10:40
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If the area of traingleular region RST is 25, what is the perimetr of RST?

1. The lenght of one side of RST is 5sq of 2
2.RST is the right isosceles triangle.
Manager
Joined: 02 Aug 2007
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1) INSUFF
We don't which side is 5 sqrt(2)
2) INSUFF
Even though that tells us the triangle has 2 equal sides and a right angle. There are numerous combinations that give us the triangle area of 25.

Together:
C. Sufficient

1) gives a side
2) tells us that two sides are equal, so base = height

Since 5 sqrt(2) cannot be the base & height with area 25, this is the hypotenuse.

Last edited by yuefei on 30 Oct 2007, 11:05, edited 1 time in total.
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Re: DS-Geometry [#permalink]  30 Oct 2007, 11:03
el1981 wrote:
If the area of traingleular region RST is 25, what is the perimetr of RST?

1. The lenght of one side of RST is 5sq of 2
2.RST is the right isosceles triangle.

i get B

since we know that RST is both a right triangle and isosceles, we can determine that both the base and the height is 5, and using the Pythagorean Thm, we can establish that the hypotenuse is 5sqt 2

so the perimeter must be 10 + 5sqrt 2
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Re: DS-Geometry [#permalink]  30 Oct 2007, 15:10
beckee529 wrote:
el1981 wrote:
If the area of traingleular region RST is 25, what is the perimetr of RST?

1. The lenght of one side of RST is 5sq of 2
2.RST is the right isosceles triangle.

i get B

since we know that RST is both a right triangle and isosceles, we can determine that both the base and the height is 5, and using the Pythagorean Thm, we can establish that the hypotenuse is 5sqt 2

so the perimeter must be 10 + 5sqrt 2

beckee, how exactly did you determine that both the base and the height is 5. Please elaborate.
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Given: Area of Triangle is 25, so 1/2 Base*Height = 25

Base*height =50

Stmt1: Length of one side can be any side of triangle so cannot be subsitituted in the above euqation. InSuff to find perimeter.

Stmt2: Rightangle isosceles triangle. Hence side is of ratio 1:1:Sqrt(2)
From this you have one value for base. solve for height. Sufficient

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