GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In the figure, ABCD is a rectangle. The area of quadrilatera
[#permalink]
17 Mar 2019, 12:39
17 Mar 2019, 12:39
Expert Reply
00:00
Question Stats:
85% (02:07) correct
14% (01:27) wrong based on 14 sessions
Hide Show timer Statistics
Attachment:
#GREpracticequestion In the figure, ABCD is a rectangle..jpg [ 22.21 KiB | Viewed 4767 times ]
In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is one-half the area of the rectangle ABCD. Which one of the following is the value of AD ?
(A) 5
(B) 6
(C) 7
(D) 12
(E) 15
Re: In the figure, ABCD is a rectangle. The area of quadrilatera
[#permalink]
20 Mar 2019, 09:31
20 Mar 2019, 09:31
1
Expert Reply
In the triangle EBD, the base is 3 and the height is AB. It's area, then, is: \(\frac{3AB}{2}\)
Similarly, in the triangle BDF, the base is 4 and the height is AB. So it's area is \(\frac{4AB}{2}\)
Both of these together, \(\frac{3AB}{2}+\frac{4AB}{2}=\frac{7AB}{2}\) form the area of quadrilateral EBFD. This is one half of the area of the rectangle ABCD.
The area of ABCD is AB*AD. So:
\(\frac{7AB}{2} = \frac{AB*AD}{2}\)
Multiply both sides by 2:
\(7AB = AB*AD\)
Divide both sides by AB:
\(7 = AD\)
Similarly, in the triangle BDF, the base is 4 and the height is AB. So it's area is \(\frac{4AB}{2}\)
Both of these together, \(\frac{3AB}{2}+\frac{4AB}{2}=\frac{7AB}{2}\) form the area of quadrilateral EBFD. This is one half of the area of the rectangle ABCD.
The area of ABCD is AB*AD. So:
\(\frac{7AB}{2} = \frac{AB*AD}{2}\)
Multiply both sides by 2:
\(7AB = AB*AD\)
Divide both sides by AB:
\(7 = AD\)
Re: In the figure, ABCD is a rectangle. The area of quadrilatera
[#permalink]
13 Aug 2022, 05:16
13 Aug 2022, 05:16
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
