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# In the diagram, find the length of AB.

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Math Expert
Joined: 02 Sep 2009
Posts: 52285
In the diagram, find the length of AB.  [#permalink]

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08 Feb 2018, 04:44
00:00

Difficulty:

55% (hard)

Question Stats:

72% (02:07) correct 28% (02:09) wrong based on 43 sessions

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In the diagram, find the length of AB .

(1) ABCD is a rectangle.

(2) AC - AE = AB + BE

Attachment:

2018-02-08_1643.png [ 8.28 KiB | Viewed 1831 times ]

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Re: In the diagram, find the length of AB.  [#permalink]

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08 Feb 2018, 07:46
Bunuel wrote:

In the diagram, find the length of AB .

(1) ABCD is a rectangle.

(2) AC - AE = AB + BE

Attachment:
2018-02-08_1643.png

Statement 1

ABCD is a rectangle and its diagonal is 5. This tells us that AB^2 + BC^2 = 5^2 = 25
But since multiple values are possible for AB and BC, we cannot find a unique value of AB. Not sufficient.
(eg., we can have AB=4, BC=3 or we can also have both AB = BC = 5/√2)

Statement 2

AC - AE = AB + BE. This can also be written as:
AC = AB + BE + AE. Now BE+AE is nothing but AB only. So replacing it we get
AC = AB + AB = 2*AB or AB = AC/2
Since we already have the value of AC, AB can be determined. Sufficient.

Re: In the diagram, find the length of AB. &nbs [#permalink] 08 Feb 2018, 07:46
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