GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2019, 22:01

### GMAT 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In the figure above, the area of square ABCF is 25 and triangle CGD is

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58472
In the figure above, the area of square ABCF is 25 and triangle CGD is  [#permalink]

### Show Tags

16 Mar 2018, 00:04
00:00

Difficulty:

15% (low)

Question Stats:

95% (01:25) correct 5% (01:51) wrong based on 60 sessions

### HideShow timer Statistics

In the figure above, the area of square ABCF is 25 and triangle CGD is an isosceles right triangle. What is the area of rectangle DEFG?

A. 15
B. 12
C. 9
D. $$6\sqrt{2}$$
E. 6

Attachment:

2018-03-16_1012.png [ 8.33 KiB | Viewed 915 times ]

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58472
Re: In the figure above, the area of square ABCF is 25 and triangle CGD is  [#permalink]

### Show Tags

16 Mar 2018, 00:05
Bunuel wrote:

In the figure above, the area of square ABCF is 25 and triangle CGD is an isosceles right triangle. What is the area of rectangle DEFG?

A. 15
B. 12
C. 9
D. $$6\sqrt{2}$$
E. 6

Attachment:
2018-03-16_1012.png

For other subjects:
ALL YOU NEED FOR QUANT ! ! !
_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3332
Location: India
GPA: 3.12
Re: In the figure above, the area of square ABCF is 25 and triangle CGD is  [#permalink]

### Show Tags

16 Mar 2018, 00:37
1

Since the area of the square ABCF is 25, the side of the square is 5.

Since the triangle GCD is an isosceles right triangle, the sides are in the ratio $$1:1:\sqrt{2}$$
We are given that the hypotenuse of the triangle is $$3\sqrt{2}$$, the other sides are equal to 3.

In rectangle GFDE, GF = 5 - 3 = 2. Also, GD = 3.

Therefore, the area of the rectangle GFDE is 6(Option E)
_________________
You've got what it takes, but it will take everything you've got
Retired Moderator
Joined: 28 Mar 2017
Posts: 1195
Location: India
GMAT 1: 730 Q49 V41
GPA: 4
Re: In the figure above, the area of square ABCF is 25 and triangle CGD is  [#permalink]

### Show Tags

16 Mar 2018, 03:49
1
Bunuel wrote:

In the figure above, the area of square ABCF is 25 and triangle CGD is an isosceles right triangle. What is the area of rectangle DEFG?

A. 15
B. 12
C. 9
D. $$6\sqrt{2}$$
E. 6

Attachment:
2018-03-16_1012.png

10 second question.

Straight "E".

Isosceles right triangle has sides in the ratio 1(short):1(shhort):root2(hypo)
In the figure hypot=3*root2
So short side = 3
Now for rectabgle:
l=3 b=2
Area=6
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8147
Location: United States (CA)
Re: In the figure above, the area of square ABCF is 25 and triangle CGD is  [#permalink]

### Show Tags

19 Mar 2018, 16:13
Bunuel wrote:

In the figure above, the area of square ABCF is 25 and triangle CGD is an isosceles right triangle. What is the area of rectangle DEFG?

A. 15
B. 12
C. 9
D. $$6\sqrt{2}$$
E. 6

Attachment:
2018-03-16_1012.png

Since triangle CGD is an isosceles right triangle (i.e., 45-45-90), both sides CG and GD = 3√2/√2 = 3. Since the area of square ABCF is 25, side CF = √25 = 5. Thus side GF is 5 - 3 = 2.

Finally, the area of rectangle DEFG is GF x GD = 2 x 3 = 6.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3092
Re: In the figure above, the area of square ABCF is 25 and triangle CGD is  [#permalink]

### Show Tags

25 Mar 2018, 12:02

Solution

•Area of square $$ABCF= 25$$

Let us assume the length of the sides of the square is ‘$$a$$’, then:

•$$a^2=25$$
•$$a=5$$ (Distance cannot be negative so $$a$$ cannot be $$-5$$)

•Triangle $$GCD$$ is an isosceles right-angled triangle.
•GCD is $$45- 45- 90$$ triangle.
•$$GC:GD: DC$$= $$1:1:\sqrt{2}$$
GC= GD= $$3$$

•Since $$GD=FE$$, hence $$FE=3$$.
•Since $$CF= AB=CG + GF$$ = $$5$$, hence GF=$$2$$.

Area of rectangle $$DEFG= FE*GF$$
= $$3*2=6$$

_________________
Re: In the figure above, the area of square ABCF is 25 and triangle CGD is   [#permalink] 25 Mar 2018, 12:02
Display posts from previous: Sort by