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# In the diagram find the length of AB?

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Math Expert
Joined: 02 Sep 2009
Posts: 60555
In the diagram find the length of AB?  [#permalink]

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11 Nov 2019, 04:41
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Difficulty:

35% (medium)

Question Stats:

52% (01:26) correct 48% (01:31) wrong based on 20 sessions

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In the diagram find the length of AB?

(1) ABCD is a rectangle
(2) AC - AE = AB + BE

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Math Expert
Joined: 02 Aug 2009
Posts: 8340
Re: In the diagram find the length of AB?  [#permalink]

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11 Nov 2019, 08:45
In the diagram find the length of AB?

(1) ABCD is a rectangle

(2) AC - AE = AB + BE
You don't require to draw anything, just solve the equation...
$$AC - AE = AB + BE...AC=AB+BE+AE=AB+AB$$, as $$AB=AE+BE$$
so $$AB=\frac{AC}{2}=\frac{5}{2}=2.5$$

B
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Re: In the diagram find the length of AB?  [#permalink]

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11 Nov 2019, 09:59
In the diagram find the length of AB?

(1) ABCD is a rectangle
Either AB > BC or BC > AB.
Since variable possibility exists, unique answer not possible. Also, nothing about AB & BC is given.

INSUFFICIENT.

(2) AC - AE = AB + BE
AC = AB + BE + AE
AC = AB + AB
AC = 2 AB
AB = AC / 2 = 5/2 = 2.5

SUFFICIENT.

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Re: In the diagram find the length of AB?   [#permalink] 11 Nov 2019, 09:59
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