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# If the figure above shows the diagonal of two rectangles, is the inner

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Math Expert
Joined: 02 Sep 2009
Posts: 50572
If the figure above shows the diagonal of two rectangles, is the inner  [#permalink]

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13 Sep 2018, 04:11
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:14) correct 33% (01:32) wrong based on 21 sessions

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If the figure above shows the diagonal of two rectangles, is the inner rectangle a square?

(1) The outer rectangle is a square.
(2) The ratio of a side of the outer rectangle to its area is is x:x^2

Attachment:

image009.jpg [ 3.76 KiB | Viewed 399 times ]

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Joined: 19 Apr 2017
Posts: 40
Re: If the figure above shows the diagonal of two rectangles, is the inner  [#permalink]

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15 Sep 2018, 03:46
If the figure above shows the diagonal of two rectangles, is the inner rectangle a square?
The diagonals in a square are always 45 degrees, if we can prove the diagonal is at 45 degree we find the answer

(1) The outer rectangle is a square means the diagonal splits the square into two 45 45 90 triangle = a, a, a√2
Since the diagonal is 45 then the inner rectangle is also a square

(2) The ratio of a side of the outer rectangle to its area is is x:x^2

$$side:area = x:x^2$$

$$side/(side^2) = x:x^2$$

means the area is side times side which is not true for rectangle but true for square
sufficient

D
Re: If the figure above shows the diagonal of two rectangles, is the inner &nbs [#permalink] 15 Sep 2018, 03:46
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