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The area of rectangle ABCD is closest to which of the following?

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The area of rectangle ABCD is closest to which of the following?  [#permalink]

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New post 07 May 2015, 04:05
00:00
A
B
C
D
E

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  35% (medium)

Question Stats:

68% (00:41) correct 32% (00:56) wrong based on 135 sessions

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The area of rectangle ABCD is closest to which of the following?

(A) 100
(B) 130
(C) 170
(D) 200
(E) 230

Attachment:
drawn-1.png
drawn-1.png [ 4.01 KiB | Viewed 2119 times ]


Kudos for a correct solution.

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The area of rectangle ABCD is closest to which of the following?  [#permalink]

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New post Updated on: 07 May 2015, 06:56
1
Let length be: L
tan 30 deg = 10/L

Since, tan 30 deg = 1/\(\sqrt{3}\)

1/\(\sqrt{3}\) = 10/L


L = 10*\(\sqrt{3}\)
(\(\sqrt{3}\) ~ 1.732)
Therefore, L = 17.32

Now, area is 10*L, ie. 10*17.32 = 173.2 ~ 170

Answer: C

Originally posted by ApurbaGMAT on 07 May 2015, 06:49.
Last edited by ApurbaGMAT on 07 May 2015, 06:56, edited 1 time in total.
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Re: The area of rectangle ABCD is closest to which of the following?  [#permalink]

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New post 07 May 2015, 06:55
1
As we know that Arc ACD is 30 degrees and arc DAC is 90 degrees we can infer that the remaining arc in the upper right area has to be 60 degrees as a triangle has a maximum of 180 degrees.

This yields a 30-60-90 triangle with side relationship of x - x sqrt 3 - 2x. X in this case is 10, therefore we can derive the other sides and also the bottom side of the rectangle.

In my calculation this results in an area of approx. 170!
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Re: The area of rectangle ABCD is closest to which of the following?  [#permalink]

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New post 07 May 2015, 09:15
1
Bunuel wrote:
Image
The area of rectangle ABCD is closest to which of the following?

(A) 100
(B) 130
(C) 170
(D) 200
(E) 230

Attachment:
drawn-1.png


Kudos for a correct solution.


Triangle ABC or ACD are 30-60-90 triangle, thus, AD= \(a\sqrt{3} = 10\sqrt{3} = 17 => Area = 10*17 = 170\)

Hence Answer is C
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The area of rectangle ABCD is closest to which of the following?  [#permalink]

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New post 11 May 2015, 04:01
Bunuel wrote:
Image
The area of rectangle ABCD is closest to which of the following?

(A) 100
(B) 130
(C) 170
(D) 200
(E) 230

Attachment:
drawn-1.png


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

Suppose we don't know the math to answer this question. We are told it's a rectangle, so we know the angles must be right angles, and we know the area must be length (AD) times height (AB). We know the height is 10. We know AD is drawn to scale. It definitely is longer than AB, so the area is definitely larger than 10 x 10 (answer (A) is out). AD doesn't look as long as twice AB, so the area is definitely less than 10 x 20 (answers (D) & (E) are out). Notice, with pure spatial estimation, we eliminated three of the five answer choices, so it will be to our advantage to guess randomly from the remaining two if we can't decide between them. Estimating from size can be a huge help if you don't remember the way to solve the problem.

BTW, the real math solution to that question: from the properties of the 30-60-90 triangle (ACD), we know that \(AD = 10*\sqrt{3}\), and since \(\sqrt{3}\) is approximately 1.7, AD is approximately 17, and the area is approximately 170.

Answer = C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: The area of rectangle ABCD is closest to which of the following?  [#permalink]

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New post 10 Jan 2018, 19:24
Bunuel wrote:
Image
The area of rectangle ABCD is closest to which of the following?

(A) 100
(B) 130
(C) 170
(D) 200
(E) 230

Attachment:
drawn-1.png


Kudos for a correct solution.

--------------------
Let the length of the diagonal be h.
h*cos 60 = 10 (=b)
h*(1/2)=10
h=20

l*l + b*b =20*20
since b =10
=> l = 10 * sqrt(3)
Area =l*b = 10 * sqrt(3) * 10
=100 * sqrt(3)
=100 * 1.732
=173.2 closest to 170
Re: The area of rectangle ABCD is closest to which of the following? &nbs [#permalink] 10 Jan 2018, 19:24
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