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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 15 Mar 2018, 12:12
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Question Stats:

69% (02:43) correct 31% (03:34) wrong based on 27 sessions

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If ABCD is a rectangle, then what is the length of EC?
Attachment:
Capture1.JPG
Capture1.JPG [ 16.74 KiB | Viewed 377 times ]


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

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

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New post 15 Mar 2018, 15:37
From Pythagorean theorem the diagonal \(BD = \sqrt{12^2 + 16^2} = \sqrt{400} = 20\)
Let \(ED = x\), and \(EB = 20 - x\)

Then, we have two equations:
(1) \(EC^2 + (20-x)^2 = 16^2\)
(2) \(EC^2 + x^2 = 12^2\)

Solving equation 2 we get:
\(EC^2 + 400 - 40x + x^2 = 256\)
\(EC^2 +x^2 - 40x = -144\)

Substracting equation (1) from (2) results in:
\(40x = 288; x = 7.2\)

Then, from triangle DEC -
\(7.2^2 + EC^2 = 12^2\)
\(51.84 + EC^2 = 144\)
\(EC = \sqrt{92.16}\)

We do not need to calculate we can use the answers. \(\sqrt{92.16}\) is obviously more than 9, since \(9^2 = 81\) hence the only answer suitable is \(EC = 9.6\)

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

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New post 15 Mar 2018, 18:48
We can see that Tr BAD is a right angled triangle with two sides 12 and 16.
Now, we know (3, 4, 5) as a set of sides for a right angled triangle. Multiply each by 4, we get (12, 16, 20)

So, the side BD is 20.

Area of Tr BCD is half of the area of Rec ABCD

1/2*BD*EC = 1/2*AD*CD

1/2*20*EC = 1/2*12*16

EC = 9.6cm

itisSheldon wrote:
If ABCD is a rectangle, then what is the length of EC?
Attachment:
Capture1.JPG


(A) 7.8
(B) 8
(C) 8.4
(D) 9
(E) 9.6
GMAT Club Bot
Re: If ABCD is a rectangle, then what is the length of EC? &nbs [#permalink] 15 Mar 2018, 18:48
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If ABCD is a rectangle, then what is the length of EC?

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