Triangle

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grandh01: Master | Next Rank: 500 Posts; Posts: 265; Joined: Tue Jul 03, 2012 11:04 pmFollowed by: 6 members

by grandh01 » Sun Aug 19, 2012 6:45 pm

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

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Source: Beat The GMAT — Data Sufficiency | Sun Aug 19, 2012 6:45 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Aug 19, 2012 6:55 pm

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) * xÂ²
xÂ² = 50 implies x = âˆš50
By Pythagoras Theorem, xÂ² + xÂ² = yÂ² or yÂ² = 2xÂ²
So, yÂ² = 2xÂ² = 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.

Last edited by Anurag@Gurome on Sun Aug 19, 2012 10:40 pm, edited 1 time in total.

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anuprajan5: Master | Next Rank: 500 Posts; Posts: 279; Joined: Mon Jun 25, 2012 10:56 pmFollowed by: 10 members; Thanked: 60 times

by anuprajan5 » Sun Aug 19, 2012 10:39 pm

Anurag,

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

Regards
Anup

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Aug 19, 2012 10:42 pm

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

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