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DS - Triangles

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by ccassel » Fri Apr 01, 2011 8:10 am
How would you explain your answer for this question?

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

(1) The length of one side of RST is 5sqrt2
(2) RST is a right isosceles triangle
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Source: — Data Sufficiency |
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by kmittal82 » Fri Apr 01, 2011 8:20 am
I think its (B)

(1) Clearly not enough information here

(2) Area of Rt isosceles triangle = (1/2) X RT x RS (You can change these depending on where u put ur points)

Since its isoceles, RT = RS

Area = (1/2) x (RT) ^ 2
Area = 50, which gives us RT = 5sqrt(2), which in turn gives us RS, which in turn allows you to calculate ST (hypotenuse)
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by manpsingh87 » Fri Apr 01, 2011 8:32 am
ccassel wrote:How would you explain your answer for this question?

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

(1) The length of one side of RST is 5sqrt2
(2) RST is a right isosceles triangle
statement1 is not sufficient to answer the question,

as RST is a right isosceles triangle, let length of equal sides be x, therefore area = 1/2*x^2=25;
x^2=50; x=sqrt(50); x=5sqrt(2);
now by using Pythagoras theorem we have x^2+x^2=h^2;
2x^2=h^2;h^2=100; h=10, hence perimeter =10sqrt(2)+10=10(sqrt(2)+1);as statement 2 alone is sufficient to answer the question,hence B
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