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Geo - Rt triangle

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hemant_rajput: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 22, 2012 7:13 amFollowed by: 13 members; Thanked: 46 times; GMAT Score:700

by hemant_rajput » Thu Jul 04, 2013 9:58 am

The perimeter of a certain isosceles right triangle is 32 + 32 2âˆš. What is the length of the hypotenuse of the triangle?
(A)16
(B)32
(C)8 root(3)
(D)8 root(2)
(E)16 root(2)

I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.

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Source: Beat The GMAT — Problem Solving | Thu Jul 04, 2013 9:58 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jul 04, 2013 10:16 am

hemant_rajput wrote:The perimeter of a certain isosceles right triangle is 32 + 32 âˆš2. What is the length of the hypotenuse of the triangle?
(A)16
(B)32
(C)8 root(3)
(D)8 root(2)
(E)16 root(2)

EDIT: I deleted my post. I had assumed that the question was identical to this popular question:
https://www.beatthegmat.com/relation-bet ... tml#700804

Cheers,
Brent

Last edited by Brent@GMATPrepNow on Wed Nov 06, 2013 6:54 am, edited 1 time in total.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jul 04, 2013 10:34 am

hemant_rajput wrote:The perimeter of a certain isosceles right triangle is 32 + 32 âˆš2. What is the length of the hypotenuse of the triangle?
(A)16
(B)32
(C)8 root(3)
(D)8 root(2)
(E)16 root(2)

EDIT: I deleted my post. I had assumed that the question was identical to this popular question:
https://www.beatthegmat.com/relation-bet ... tml#700804

Cheers,
Brent

Last edited by Brent@GMATPrepNow on Wed Nov 06, 2013 6:55 am, edited 1 time in total.

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jul 04, 2013 10:37 am

hemant_rajput wrote:The perimeter of a certain isosceles right triangle is 32 + 32âˆš2. What is the length of the hypotenuse of the triangle?

(A)16
(B)32
(C)8 root(3)
(D)8 root(2)
(E)16 root(2)

The sides of an isosceles right triangle are proportioned: s : s : sâˆš2.
So if s=side and h=hypotenuse, then h = sâˆš2 and s = h/âˆš2.

We can plug in the answers, which represent the hypotenuse.
The correct answer is unlikely to be C, since âˆš3 is not a value typically attributed to an isosceles right triangle.

Answer choice D: h = 8âˆš2
s = (8âˆš2)/âˆš2 = 8.
p = 8 + 8 + 8âˆš2 = 16 + 8âˆš2.
Eliminate D. The perimeter needs to be quite a bit larger.

Answer choice B: h = 32
s = 32/âˆš2 = (32*âˆš2)/(âˆš2*âˆš2) = (32âˆš2)/2 = 16âˆš2.
p = 16âˆš2 + 16âˆš2 + 32 = 32 + 32âˆš2. Success!

The correct answer is B.

Last edited by GMATGuruNY on Thu Jul 18, 2013 2:13 am, edited 1 time in total.

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kuzzden: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Tue Apr 09, 2013 9:00 pm; GMAT Score:700

by kuzzden » Wed Jul 10, 2013 12:31 am

Hi, maybe simple algebraic method will also help:

Since the triangle is isosceles, its P = 2x + y
since it is right y*y = 2x*x, since all values are positive
x= y / sqr(2) = y*sqr(2)/2

Finally, after substitution we get P = y + y* sqr(2) = 32 + 32*sqr(2)
So, y = 32

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macattack: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Wed Jun 26, 2013 10:55 pmFollowed by: 1 member; Thanked: 11 times

by macattack » Thu Jul 18, 2013 1:22 am

Hi experts,
you gave two dissimilar answers!!!! I think Mitch got it right!
Cheers

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