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# In the figure, ABCD is a rectangle, and F and E are points on AB and B

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Math Expert
Joined: 02 Sep 2009
Posts: 59725
In the figure, ABCD is a rectangle, and F and E are points on AB and B  [#permalink]

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17 Mar 2019, 23:53
00:00

Difficulty:

15% (low)

Question Stats:

100% (01:25) correct 0% (00:00) wrong based on 10 sessions

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In the figure, ABCD is a rectangle, and F and E are points on AB and BC, respectively. The area of ∆DFB is 9 and the area of ∆BED is 24. What is the perimeter of the rectangle?

(A) 18

(B) 23

(C) 30

(D) 42

(E) 48

Attachment:

#GREpracticequestion In the figure, ABCD is a rectangle, and F and E are points.jpg [ 22.91 KiB | Viewed 372 times ]

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Re: In the figure, ABCD is a rectangle, and F and E are points on AB and B  [#permalink]

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18 Mar 2019, 02:09
Bunuel wrote:

In the figure, ABCD is a rectangle, and F and E are points on AB and BC, respectively. The area of ∆DFB∆DFB is 9 and the area of ∆BED is 24. What is the perimeter of the rectangle?

(A) 18

(B) 23

(C) 30

(D) 42

(E) 48

Attachment:
#GREpracticequestion In the figure, ABCD is a rectangle, and F and E are points.jpg

area of triagnle DFC = 9
1/2 ×FB ×AD. We are given that the area of ∆DFB is 9. Hence, we have

1/2 × FB ×AD = 9

1/2 × 2 × AD = 9

Area of ∆BED
1/2 × BE ×DC = 24

1/2 × 4 × DC = 24

from the figure, BE = 4

DC = 12

Now, the formula for the perimeter of a rectangle is

2(AD +DC) = 2(9 + 12) = 2 × 21 = 42.
IMO D
Re: In the figure, ABCD is a rectangle, and F and E are points on AB and B   [#permalink] 18 Mar 2019, 02:09
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