Data Sufficiency

grandh01 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 square root 2.
(2) RST is a right isosceles triangle.

OA is B

(1) The length of one side of RST is 5 square root 2. This is clearly NOT sufficient, as we do not know the measurement of other sides of triangle RST.

(2) RST is a right isosceles triangle.
Let us assume that the two equal sides of triangle RST = x units each
and the hypotenuse = y units
Area of triangle = (1/2) * base * height
25 = (1/2) * x²
x² = 50 implies x = √50
By Pythagoras Theorem, x² + x² = y² or y² = 2x²
So, y² = 2x² = 2 * 50 = 100
y = 10
We know the values of x and y, hence we can find the perimeter of triangle RST; SUFFICIENT.

The correct answer is B.

anuprajan5 wrote:Anurag,

I know this can be misconstrued as nitpicking but for B, y = 10 and not y = 10^1/2

Regards
Anup

Thanks for pointing this, have corrected that