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# In the figure above, ABCD is a rectangle and E is the midpoint of one

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Math Expert
Joined: 02 Sep 2009
Posts: 51122
In the figure above, ABCD is a rectangle and E is the midpoint of one  [#permalink]

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24 Jan 2016, 05:25
00:00

Difficulty:

25% (medium)

Question Stats:

85% (01:25) correct 15% (02:07) wrong based on 40 sessions

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In the figure above, ABCD is a rectangle and E is the midpoint of one side. What is the area of triangle BCD?

(1) BE = 5 inches
(2) CD = 3 inches

Attachment:

2016-01-24_1724.png [ 4.84 KiB | Viewed 4032 times ]

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Joined: 26 Mar 2013
Posts: 1910
Re: In the figure above, ABCD is a rectangle and E is the midpoint of one  [#permalink]

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25 Jan 2016, 10:30
Bunuel wrote:

In the figure above, ABCD is a rectangle and E is the midpoint of one side. What is the area of triangle BCD?

(1) BE = 5 inches
(2) CD = 3 inches

Attachment:
2016-01-24_1724.png

To get area, we need to know CD &BC

1) BE=5...insuff
2) CD =3 ...insuff

Combine 1 &2

triangle BAE is right angle , hence AE= 4 so AD =8 inch=BC

So we can get area

Intern
Joined: 07 Oct 2014
Posts: 9
In the figure above, ABCD is a rectangle and E is the midpoint of one  [#permalink]

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25 Jan 2016, 11:41
In order to determine the square of the right triangle we need to know the measures of at least two of its sides (any), or a measure of a side and that of an angle (any except for the right one). Thus, in order to determine the square of BCD, which is equal to ABD, we need to know any two of the following sides: AB, BD or AB.

(1) Not sufficient.
BE alone doesn't give us the exact measures for AB and AE
(2) Not sufficient.
CD (=AB) is the only one side, and one side is not enough to determine the square

(1) & (2). Sufficient.
BE and CD give us AE. AD=2AE. AB and AD are enough to calculate the square of BCD.

Thus, C.
In the figure above, ABCD is a rectangle and E is the midpoint of one &nbs [#permalink] 25 Jan 2016, 11:41
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