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555-605 (Medium)|   Geometry|      
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Bunuel
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In the figure above, rectangle ABCD has perimeter 22; the length of DC 07 Feb 2016, 10:29
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C
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76% (01:59) correct 24% (02:00) wrong based on 124 sessions

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In the figure above, rectangle ABCD has perimeter 22; the length of DC is 7. What is the area of DEF?

A. 12
B. \(8 \sqrt{3}\)
C. 24
D. 32
E. 64

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C
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In the figure above, rectangle ABCD has perimeter 22; the length of DC 09 Feb 2016, 20:11
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Bunuel

In the figure above, rectangle ABCD has perimeter 22; the length of DC is 7. What is the area of ODEF?

A. 12
B. \(8 \sqrt{3}\)
C. 24
D. 32
E. 64

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Hi Bunuel, I think we need the area of ADEF here and not ODEF.
Can you please check it once.
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In the figure above, rectangle ABCD has perimeter 22; the length of DC 09 Feb 2016, 22:44
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Bunuel

In the figure above, rectangle ABCD has perimeter 22; the length of DC is 7. What is the area of ODEF?

A. 12
B. \(8 \sqrt{3}\)
C. 24
D. 32
E. 64

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Attachment:
2016-02-07_2128.png
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I am assuming we are looking for the area of the triangle DEF (if we needed the area of quad ADEF, we would have written it as ADFE so guessing that O is a typo).

Since ABCD is a rectangle and CD is 7, AB is also 7.
The perimeter of ABCD is 22 so BC + AD = 22 - 7*2 = 8
Since BC = AD, AD = 4

Triangle ADE is a 30-60-90 triangle so sides are in the ratio \(1:\sqrt{3}:2\).
Since AD = 4, DE = \(4*\sqrt{3}\)

Tringle DEF is 45-45-90 triangle so the two legs are equal in length. Since DE is \(4*\sqrt{3}\), EF is also \(4*\sqrt{3}\).

Area of DEF = \((1/2)*4*\sqrt{3}*4*\sqrt{3} = 24\)

Answer (C)
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In the figure above, rectangle ABCD has perimeter 22; the length of DC 09 Feb 2016, 22:53
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OptimusPrepJanielle
Bunuel

In the figure above, rectangle ABCD has perimeter 22; the length of DC is 7. What is the area of ODEF?

A. 12
B. \(8 \sqrt{3}\)
C. 24
D. 32
E. 64

Show Spoiler
Attachment:
2016-02-07_2128.png
Hi Bunuel, I think we need the area of ADEF here and not ODEF.
Can you please check it once.
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Edited. It's DEF not ODEF. Thank you.
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In the figure above, rectangle ABCD has perimeter 22; the length of DC 11 Feb 2016, 07:05
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\(DA = 4\)
\(DE = EF = 4\sqrt{3}\)
so answer C
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In the figure above, rectangle ABCD has perimeter 22; the length of DC 11 Feb 2016, 08:01
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30 ,60 ,90 triangle and 45 , 45 , 90 triangle are quit common from gmat point. first we will find the othr side and then using this combination we can find requird value. Since ABCD is a rectangle and CD is 7, AB is also 7.
The perimeter of ABCD is 22 so BC + AD = 22 - 7*2 = 8
Since BC = AD, AD = 4

Triangle ADE is a 30-60-90 triangle so sides are in the ratio 1:3√:21:3:2.
Since AD = 4, DE = 4∗3√4∗3

Tringle DEF is 45-45-90 triangle so the two legs are equal in length. Since DE is 4∗3√4∗3, EF is also 4∗3√4∗3.

Area of DEF = (1/2)∗4∗3√∗4∗3√=24(1/2)∗4∗3∗4∗3=24
, so correct answer is c. please give kudos ..it motivates you...
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In the figure above, rectangle ABCD has perimeter 22; the length of DC 11 Feb 2016, 23:09
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use of pythogorous triplets:
rectangle ABCD:
14 + 2x = 22
2x = 8
x = 4

using pythogorous triplets 30:60:90 = x: xsqrt3 : 2x

we know side DE is 4sqrt3

using pythogorous triplets 45:45:90 = x: x : xsqrt2 = : 4sqrt3 : 4sqrt6

Area = 1/2 x base x height = 24
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In the figure above, rectangle ABCD has perimeter 22; the length of DC 22 Oct 2020, 12:57
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