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ABC is a right triangle with legs of length x/y

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ABC is a right triangle with legs of length x/y [#permalink] New post   28 Dec 2021, 06:24
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ABC is a right triangle with legs of length \(\frac{x}{y}\) and \(y\)

Quantity A
Quantity B
\(\frac{x[5-\sqrt{17}][\sqrt{17}+5]}{\sqrt{256}}\)
The area of triangle ABC




The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
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ABC is a right triangle with legs of length x/y [#permalink] New post   28 Dec 2021, 11:33
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Quantity A:

\(\frac{x(5−√17)(√17+5)}{√256} = \frac{(5x−x√17)(√17+5)}{√256} = \frac{(5x√17 + 25 x - 17 x - 5x√17)}{√256} = \frac{8x}{√256} = \frac{8x}{16} = \frac{x}{2}\)

Quantity B:

Area of ABC = ( y * [x/y] )/2 = \(\frac{x}{2}\)

Answer:

Qty A = Qty B = \(\frac{x}{2}\)
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ABC is a right triangle with legs of length x/y [#permalink]
28 Dec 2021, 11:33
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