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

 It is currently 09 Dec 2018, 20:20

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

December 09, 2018

December 09, 2018

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# The area of square ABDE in the figure above is 100. If BC = CD, what

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51035
The area of square ABDE in the figure above is 100. If BC = CD, what  [#permalink]

### Show Tags

11 Nov 2017, 05:41
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:24) correct 27% (01:24) wrong based on 24 sessions

### HideShow timer Statistics

The area of square ABDE in the figure above is 100. If BC = CD, what is the perimeter of ∆ BCD?

(A) 5√2 + 10
(B) 20
(C) 10√2 + 10
(D) 30
(E) 20√2 + 10

Attachment:

2017-11-10_1035_001.png [ 4.73 KiB | Viewed 647 times ]

_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 2197
The area of square ABDE in the figure above is 100. If BC = CD, what  [#permalink]

### Show Tags

11 Nov 2017, 07:44
Bunuel wrote:

The area of square ABDE in the figure above is 100. If BC = CD, what is the perimeter of ∆ BCD?

(A) 5√2 + 10
(B) 20
(C) 10√2 + 10
(D) 30
(E) 20√2 + 10

Attachment:
2017-11-10_1035_001.png

Area of square = s$$^2$$ = 100
s = 10
BD = 10

∆ BCD has a right angle and two equals sides (BC = CD).
∆ BCD is a right isosceles triangle with side lengths in ratio $$x: x: x\sqrt{2}$$

Sides BC and CD correspond with $$x$$
Side BD corresponds with $$x\sqrt{2}$$

$$x\sqrt{2} = 10$$

$$x =\frac{10}{\sqrt{2}}$$

$$x=\frac{10}{\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}}=\frac{10\sqrt{2}}{2}=5\sqrt{2}$$

$$x=5\sqrt{2}$$ = BC = CD

Perimeter P of ∆ BCD = BC + CD + BD

P = $$5\sqrt{2} + 5\sqrt{2} + 10 =$$
P = $$10\sqrt{2} + 10$$

The area of square ABDE in the figure above is 100. If BC = CD, what &nbs [#permalink] 11 Nov 2017, 07:44
Display posts from previous: Sort by