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

 It is currently 15 Oct 2019, 19:15

### 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

# If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58340
If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of  [#permalink]

### Show Tags

07 Feb 2019, 02:51
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:29) correct 34% (01:42) wrong based on 35 sessions

### HideShow timer Statistics

If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of the circle, in terms of x, is

A. $$\sqrt{3} x\pi$$

B. $$\sqrt{5} x\pi$$

C. $$\sqrt{3x} \pi$$

D. $$\sqrt{5x} \pi$$

E. $$5x^2 \pi$$

Attachment:

Geometry_015.jpg [ 8.72 KiB | Viewed 884 times ]

_________________
Director
Joined: 09 Mar 2018
Posts: 996
Location: India
Re: If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of  [#permalink]

### Show Tags

07 Feb 2019, 03:09
Bunuel wrote:

If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of the circle, in terms of x, is

A. $$\sqrt{3} x\pi$$

B. $$\sqrt{5} x\pi$$

C. $$\sqrt{3x} \pi$$

D. $$\sqrt{5x} \pi$$

E. $$5x^2 \pi$$

If ABCD is a rectangle, lets calculate AC

AC =$$\sqrt{{x^2 + 4* x^2}}$$
AC = $$\sqrt{5}$$x

AC will be the diameter, radius will be $$\sqrt{5}$$x / 2

C = 2 $$\pi r$$
= 2 * $$\pi$$$$\sqrt{5}$$x / 2
= $$\sqrt{5} x\pi$$
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Senior Manager
Joined: 13 Jan 2018
Posts: 342
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23
GMAT 2: 640 Q49 V27
GPA: 4
WE: Consulting (Consulting)
Re: If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of  [#permalink]

### Show Tags

07 Feb 2019, 03:12
Attachment:

image.jpg [ 28.22 KiB | Viewed 688 times ]

From the above fig, the diagonal of the rectangle serves as the diameter of the circle as the diagonal passes through the center of both the circle and the rectangle.

Since the diameter is of $$\sqrt{5}x$$, radius of the circle $$\frac{\sqrt{5}x}{2}$$

The circumference of a circle is $$2\pi r$$ = $$2*\pi*\frac{\sqrt{5}x}{2}$$

$$\sqrt{5}x \pi$$

OPTION: B
_________________
____________________________
Regards,

Chaitanya

+1 Kudos

if you like my explanation!!!
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4999
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of  [#permalink]

### Show Tags

07 Feb 2019, 03:52
diaganol of the rectangle = diameter of circle
d of rectangle = \sqrt{5}x

2 * pi * \sqrt{5}x/2

=>$$\sqrt{5} x\pi$$
IMO B

Bunuel wrote:

If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of the circle, in terms of x, is

A. $$\sqrt{3} x\pi$$

B. $$\sqrt{5} x\pi$$

C. $$\sqrt{3x} \pi$$

D. $$\sqrt{5x} \pi$$

E. $$5x^2 \pi$$

Attachment:
Geometry_015.jpg
Re: If ABCD is a rectangle, BC = x and AB = 2x, then the circumference of   [#permalink] 07 Feb 2019, 03:52
Display posts from previous: Sort by