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Triangle - DS

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by karthikpandian19 » Wed Dec 14, 2011 12:47 am
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*Sqroot 2
(2) RST is a right isosceles triangle.
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Source: — Data Sufficiency |
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by rijul007 » Wed Dec 14, 2011 1:10 am
karthikpandian19 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*Sqroot 2
(2) RST is a right isosceles triangle.

(1) The length of one side of RST is 5*Sqroot 2


We dont know what kind of triangle it is...
The data is insufficient



(2) RST is a right isosceles triangle.[/quote]


Area = 1/2 a*a [a is the length of base and height]
a = 5*root(2)
Hypotenuse= 10

Perimeter = 10+ 10*root(2)


Sufficient


Option B
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by Anurag@Gurome » Wed Dec 14, 2011 2:35 am
karthikpandian19 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*Sqroot 2
(2) RST is a right isosceles triangle.
To find the perimeter, we should know the length of all three sides.

(1) Length of one side = 5√2, but we do not know the length of the other sides; NOT sufficient.

(2) RST is a right angled isosceles triangle with an area of 25 sq units. If the two equal sides are x units each, then (1/2)(x)(x) = 25 or x² = 50, so we know the value of x now. Using Pythagoras Theorem, we can find the length of the 3rd side and hence the perimeter; SUFFICIENT.

The correct answer is B.
Anurag Mairal, Ph.D., MBA
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