Geometry question

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prernamalhotra: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed Apr 02, 2014 2:01 amFollowed by: 1 member; Thanked: 2 times

by prernamalhotra » Sat May 10, 2014 1:32 am

A certain right angle triangle has sides x,y,z where x<y<z. If the area of this triangular region is 1, which of the following indicates all possible values of y.

A) y < âˆš2
B) âˆš3/2<y<âˆš2
C) âˆš2/3<y<âˆš3/2
D) âˆš3/4<y<âˆš2/3
E) y<âˆš3/4

Thank you,
Prerna

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Source: Beat The GMAT — Problem Solving | Sat May 10, 2014 1:32 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 » Sat May 10, 2014 1:47 am

A certain right triangle has sides of length x, y, and z, where x < y < z.lf the area of this triangular region is 1, which of the following indicates all of the possible values of y?

(A) y > âˆš2
(B) âˆš3/2 < y < âˆš2
(C) âˆš2/3 < y < âˆš3/2
(D) âˆš3/4 < y < âˆš2/3
(E) y < âˆš3/4

Here's one approach:

Since the triangle is a right triangle, the longest side will be the hypotenuse.
This means the side with length z is the hypotenuse, and the sides with lengths x and y are the legs.

Since the legs must meet at a right angle (since this is a right triangle), we can let one side (x or y) be the base of the triangle and the other side (x or y) can be the height.

We know that area = (base)(height)/2, and we're told the area of this particular triangle is 1.
So, we can conclude that (x)(y)/2 = 1
We can rewrite this as xy = 2

Now we also need to keep in mind that x < y

Given this, we could have x=0.1 and y=20, or we could have x=0.001 and y=2000, and so on.

As you can see, we can make y as large as we wish.
So, we can eliminate answer choices B, C, D and E since they all limit the upper value of y.

Answer = A

Cheers,
Brent

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 » Sat May 10, 2014 2:26 am

Answer choice A should read as I've posted it below:

A certain right angle triangle has sides x,y,z where x<y<z. If the area of this triangular region is 1, which of the following indicates all possible values of y.

A) y > âˆš2
B) âˆš3/2 < y < âˆš2
C) âˆš2/3 < y < âˆš3/2
D) âˆš3/4 < y < âˆš2/3
E) y < âˆš3/4

Plug in an easy triangle whose area is 1.
Let x=1 and y=2, so that the area of the triangle = (1/2)(1)(2) = 1.
Since it's possible that y=2, eliminate any answer choice that does not include y=2 in its range.
Eliminate B, C, D, and E.

The correct answer is A.

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