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 > ROOT2
B. ROOT3/2 < y < ROOT2
C. ROOT2/3 < y < ROOT3/2
D. ROOT3/4 < y < ROOT2/3
E. y < ROOT3/4
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value of y
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gmatmachoman
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Since x and y are the legs (i.e. the non-hypotenuse sides) of the triangle, we can assign x and y as the base and height.gmatmachoman 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 > ROOT2
B. ROOT3/2 < y < ROOT2
C. ROOT2/3 < y < ROOT3/2
D. ROOT3/4 < y < ROOT2/3
E. y < ROOT3/4
So:
Area = 1/2 * base * height
1 = 1/2 * x * y
2 = x * y
If x=y, then y would be root2. However, we know that y > x, so it must be true that y > root2.
Only A has y > root2 as a boundary... pick A!
(As an aside, there's no upward bound on y, since x could be a tiny little fraction and y could be huge; for example, we could pick:
x = 1/10000, giving us:
2 = (1/10000) * y
20000 = y.)
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There are infinitely many right triangles that have an area of 1.gmatmachoman 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 > ROOT2
B. ROOT3/2 < y < ROOT2
C. ROOT2/3 < y < ROOT3/2
D. ROOT3/4 < y < ROOT2/3
E. y < ROOT3/4
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
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Scott@TargetTestPrep
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We see that x and y must be the legs of the triangle and z must be the hypotenuse. We also see that x and y are the base and altitude of the right triangle. Using the formula for the area of a triangle: A = ½ bh, we can create the equation:gmatmachoman 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
xy/2 = 1
xy = 2
x = 2/y
We also know that x < y < z.
Substituting, we have:
2/y < y
2 < y^2
√2 < y
Answer: A
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