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Based on the figure shown, which of the following could be true?

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Bunuel
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Based on the figure shown, which of the following could be true? [#permalink] New post   18 Feb 2022, 02:30
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Based on the figure shown, which of the following could be true?

I. a = b
II. y = z
III. a^2 + b^2 = z^2 - y^2

A. None
B. I only
C. II only
D. I and III only
E. I, II, and III




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D
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kungfury42
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Based on the figure shown, which of the following could be true? [#permalink] New post   18 Feb 2022, 02:50
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I. a=b is possible, the base triangle is an isosceles right angled triangle with a=b=5/√2

II. y, 5, z form a right angled triangle with z as the hypotenuse. y can never be equal to z as hypotenuse is always greater than the other two sides.

III. a²+b²=25 (assume base triangle is a right triangle) and y²+25=z² or z²-y²=25 (right triangle given) hence, a²+b²=z²-y²

Hence, only I and III could be possible, option D.

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Based on the figure shown, which of the following could be true? [#permalink] New post   18 Feb 2022, 21:04
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Bunuel wrote:

Based on the figure shown, which of the following could be true?

I. a = b
II. y = z
III. a^2 + b^2 = z^2 - y^2

A. None
B. I only
C. II only
D. I and III only
E. I, II, and III




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I. a = b =\(\sqrt{5}\) ... Possible
II. y = z... Not possible as such a rt triangle is not possible
III. \(a^2 + b^2 = z^2 - y^2 --->\\
a^2 + b^2 = 5^2\)
Possible

Ans D

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TarunKumar1234
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Re: Based on the figure shown, which of the following could be true? [#permalink] New post   18 Feb 2022, 23:32
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We need to find could be true.

Based on the figure shown, which of the following could be true?

I. a = b -> It is possible for an isosceles triangle.
II. y = z -> Not possible, as z> y.
III. a^2 + b^2 = z^2 - y^2 -> if smaller triangle is right angled, then it is possible.

So, I think D. :)
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Re: Based on the figure shown, which of the following could be true? [#permalink]
18 Feb 2022, 23:32
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