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.
ABCE is a square, and BCDE is a parallelogram.
[#permalink]
11 Dec 2017, 02:46
11 Dec 2017, 02:46
Expert Reply
2
Bookmarks
00:00
Question Stats:
80% (00:47) correct
19% (00:53) wrong based on 21 sessions
Hide Show timer Statistics
Attachment:
parallelogram.png [ 4.67 KiB | Viewed 6048 times ]
ABCE is a square, and BCDE is a parallelogram.
Quantity A |
Quantity B |
The area of square ABCE |
The area of parallelogram BCDE |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
Re: ABCE is a square, and BCDE is a parallelogram.
[#permalink]
14 Jan 2018, 02:32
14 Jan 2018, 02:32
2
let us suppose a side of the square = s
then, the area of the square would be s^2
Diagonal BE of the square is the hypotenuse of the triangle BAC
Since the triangle is a 45-45-90 triangle the hypotenuse must measure s√2
For the parallelogram notice that the area of the parallelogram = area of triangle BCE and area of triangle CED
Side BE//CD and CE is the transversal so triangle BCE and triangle CED are similar
<BCE=<CED=90degree
<BEC=<ECD
Since the two triangle share the same side the triangles have equal length of sides. This follows
area of parallelogram = 2* area of triangle BCE
area of triangle BCE= 1/2*s*s=s^2/2
area of parallelogram = s^2/2*2= s^2
area of square = area of parallelogram
(c)
then, the area of the square would be s^2
Diagonal BE of the square is the hypotenuse of the triangle BAC
Since the triangle is a 45-45-90 triangle the hypotenuse must measure s√2
For the parallelogram notice that the area of the parallelogram = area of triangle BCE and area of triangle CED
Side BE//CD and CE is the transversal so triangle BCE and triangle CED are similar
<BCE=<CED=90degree
<BEC=<ECD
Since the two triangle share the same side the triangles have equal length of sides. This follows
area of parallelogram = 2* area of triangle BCE
area of triangle BCE= 1/2*s*s=s^2/2
area of parallelogram = s^2/2*2= s^2
area of square = area of parallelogram
(c)
Re: ABCE is a square, and BCDE is a parallelogram.
[#permalink]
14 Jan 2018, 11:51
14 Jan 2018, 11:51
Expert Reply
Added the OA. It is C.
Regards
Regards
