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The figure shows a smaller square with sides of length y ins

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The figure shows a smaller square with sides of length y ins [#permalink]  11 Dec 2017, 10:31
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square (2).jpg [ 13.22 KiB | Viewed 527 times ]

The figure shows a smaller square with sides of length y inscribed in a larger square with sides of length x. Which of the following relationships between x, y, and z must be true ?

A. $$x^2 = y^2 + z^2$$

B. $$x^2 = y^2 - z^2$$

C. $$(x-z)^2 = y^2$$

D. $$(x-y)^2 = z^2$$

E. $$(x-z)^2 + z^2 = y^2$$
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Re: The figure shows a smaller square with sides of length y ins [#permalink]  12 Dec 2017, 05:56
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Carcass wrote:
Attachment:
The attachment square (2).jpg is no longer available

The figure shows a smaller square with sides of length y inscribed in a larger square with sides of length x. Which of the following relationships between x, y, and z must be true ?

A. $$x^2 = y^2 + z^2$$

B. $$x^2 = y^2 - z^2$$

C. $$(x-z)^2 = y^2$$

D. $$(x-y)^2 = z^2$$

E. $$(x-z)^2 + z^2 = y^2$$

[Reveal] Spoiler: OA
OA in 24h

Here
we can write as the attached diagram

Now since it is square and all angles are right angle triangle

therefore by Pythagoras theorem ; y is the hypotenuse and x and (x-z) are the two legs of the triangle

$$(x-z)^2 + z^2 = y^2$$ ; which is option E
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square %282%29.jpg [ 14.92 KiB | Viewed 508 times ]

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Re: The figure shows a smaller square with sides of length y ins   [#permalink] 12 Dec 2017, 05:56
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