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triangular region

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by ska7945 » Sat Aug 23, 2008 3:38 pm
A certain right triangle has sides of length x, y, and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?

A. y>sqrt 2
b. sqrt3/2<y<sqrt2
c.sqrt2/3<y<sqrt3/2
d.sqrt3/4<y<sqrt2/3
e.y<sqrt3/4


oa a
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by carefreeamit » Sat Aug 23, 2008 9:11 pm
Area of square = 1/2 * base * height
which is 1/2 * x * y ..z has to be the hypotenuse

so 1/2 * x * y = 1
x*y = 2
now if x and y are same then x = sqrt 2 and y = sqrt 2
but x is smaller than y so y must be greater than sqrt 2.
Ans A.
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by pre-gmat » Sun Aug 24, 2008 3:14 pm
Could you explaIN me again how did you assume x and y to be sqrt2 why can't we assume x=1 and y=2.

I clearly understand ur explanation but what I was doing was x=1 and y=2 and of course i was not getting the solution.
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by carefreeamit » Sun Aug 24, 2008 4:36 pm
There are multiple possible values x and y. So I started with a value where x and y will be same and then if y has to be greater than x then y has to be greater than sqrt 2 and x has to be smaller than sqrt 2.
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by pre-gmat » Mon Aug 25, 2008 7:53 am
Thanks.
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by hazelannie » Wed Apr 27, 2016 4:08 am
since the area of this triangular region is 1, xy=2.
since x < y < z, multiple y on both side, we could get xy<y*y, therefore, y^2>2, y>sqrt(2)
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by Matt@VeritasPrep » Wed Apr 27, 2016 2:44 pm
Look for an extreme answer.

For instance, our right triangle could have sides

x = 0.1
y = 20
z = 20.0002

and area = 1.

Since 20 is greater than the maxima in B, C, D, and E, the answer can only be A.
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by Brent@GMATPrepNow » Mon Sep 11, 2017 1:16 pm
ska7945 wrote:A certain right triangle has sides of length x, y, and z, where x < y < z. If the area of this triangular region is 1, which of the following indicates all of the possible values of y ?

A. y > √2
b. (√3)/2 < y < √2
c. (√2)/3 < y < (√3)/2
d. (√3)/4 < y < (√2)/3
e. y < (√3)/4
oa a
There are infinitely many right triangles that have an area of 1.
So, one approach is to find a triangle that meets the given conditions, and see what conclusions we can draw.

Here's one such right triangle:
Image

This meets the conditions that the area is 1 AND x < y < z
With this triangle, y = 4

When we check the answer choices, only one (answer choice A) allows for y to equal 4

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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