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
triangular region
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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.
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.
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.
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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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.
- hazelannie
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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)
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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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.
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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- Brent@GMATPrepNow
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There are infinitely many right triangles that have an area of 1.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
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:
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