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A certain right triangle has sides of length x, y, and z, wh
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10 Jun 2020, 10:08
10 Jun 2020, 10:08
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51% (02:24) correct
48% (02:58) wrong based on 182 sessions
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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. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)
C. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)
D. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)
E. \(y < \frac {\sqrt {3}}{4}\)
A. \(y > \sqrt {2}\)
B. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)
C. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)
D. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)
E. \(y < \frac {\sqrt {3}}{4}\)
Re: A certain right triangle has sides of length x, y, and z, wh
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17 Aug 2020, 15:24
17 Aug 2020, 15:24
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Carcass 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. \(y > \sqrt {2}\)
B. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)
C. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)
D. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)
E. \(y < \frac {\sqrt {3}}{4}\)
A. \(y > \sqrt {2}\)
B. \(\frac {\sqrt {3}} {2} < y < \sqrt {2}\)
C. \(\frac {\sqrt {2}} {3} < y < \frac {\sqrt {3}} {2}\)
D. \(\frac {\sqrt {3}} {4} < y < \frac {\sqrt {2}} {3}\)
E. \(y < \frac {\sqrt {3}}{4}\)
So we have a right triangle, with a hypotenuse of \(z\), the long leg as \(y\), and the short leg as \(x\).
This has to satisfy \(\frac{xy}{2} = 1\), or
\(xy = 2\)
Notice that if \(x = y\), making the triangle an isosceles triangle, then \(x = \sqrt{2} = y\).
But we know this can't be true. \(y\) is the longer leg.
This means we need to make \(x\) smaller than \(\sqrt{2}\) and \(y\) bigger than \(\sqrt{2}\). The only answer that gives us \(y > \sqrt{2}\) is A
General Discussion
Re: A certain right triangle has sides of length x, y, and z, wh
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10 Jun 2020, 10:08
10 Jun 2020, 10:08
Expert Reply
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
