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If ABCD is a rectangle, then what is the length of EC?

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If ABCD is a rectangle, then what is the length of EC?  [#permalink]

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New post 21 Jun 2019, 00:07
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:55) correct 37% (03:05) wrong based on 27 sessions

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Re: If ABCD is a rectangle, then what is the length of EC?  [#permalink]

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New post 21 Jun 2019, 00:18
1
BD = 20 since BD^2 = AB^2 + BD^2.
The area of triangle BCD = 1/2 * BD* EC = 10 * EC = 1/2 * BC * CD = 1/2 * 16* 12 = 96
=> EC = 96/10 = 9.6
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Re: If ABCD is a rectangle, then what is the length of EC?  [#permalink]

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New post 21 Jun 2019, 00:48
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Bunuel wrote:
Image
If ABCD is a rectangle, then what is the length of EC?

(A) 7.8
(B) 8
(C) 8.4
(D) 9
(E) 9.6

Attachment:
Capture1.JPG


In triangle BAD, BD^2 = 12^2 + 16^2 = 144 + 256 = 400
--> BD = 20

Triangle BAD & DEC are similar with ∠D = ∠B, ∠A = ∠E
--> BD/DC = AD/EC
--> 20/12 = 16/EC
--> EC = 16*12/20 = 96/10 = 9.6

IMO Option E

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Re: If ABCD is a rectangle, then what is the length of EC?   [#permalink] 21 Jun 2019, 00:48
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