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In the floor plan of an executive's beach house above, the north and

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In the floor plan of an executive's beach house above, the north and  [#permalink]

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New post 26 Apr 2019, 01:43
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Question Stats:

64% (02:21) correct 36% (02:29) wrong based on 159 sessions

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In the floor plan of an executive's beach house above, the north and south walls of the living room are parallel. What is the floor area, in square feet, of the bedroom?


A. \(450\sqrt{3}\)

B. 450

C. \(225\sqrt{3}\)

D. 225

E. It cannot be determined from the information given.

Attachment:
2019-04-27_0141.png
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PS19502.01
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Re: In the floor plan of an executive's beach house above, the north and  [#permalink]

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New post 28 Apr 2019, 10:14
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In the floor plan of an executive's beach house above, the north and  [#permalink]

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New post 26 Apr 2019, 18:23
Bunuel wrote:
In the floor plan of an executive's beach house above, the north and south walls of the living room are parallel. What is the floor area, in square feet, of the bedroom?


A. \(450\sqrt{3}\)

B. 450

C. \(225\sqrt{3}\)

D. 225

E. It cannot be determined from the information given.

Attachment:
2019-04-27_0141.png


PS19502.01
OG2020 NEW QUESTION


Make an parallel to the titled side of the living room from 30 feet (Middle of 60 feet)

Using similarity, the third side of the triangle=2*15=30ft.

Area of the triangle=\(\sqrt{3}/4*30*30=225\sqrt{3}\) IMO, option C.
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Re: In the floor plan of an executive's beach house above, the north and  [#permalink]

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New post 27 Apr 2019, 00:45
Can you explain what do you mean by

TornDilemma
Quote:
Make an parallel to the titled side of the living room from 30 feet (Middle of 60 feet)
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Re: In the floor plan of an executive's beach house above, the north and  [#permalink]

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New post 27 Apr 2019, 05:38
bedroom area is equilateral ∆ side 30
30^2 *√3/4
IMO C \(225\sqrt{3}\)

Bunuel wrote:
Image
In the floor plan of an executive's beach house above, the north and south walls of the living room are parallel. What is the floor area, in square feet, of the bedroom?


A. \(450\sqrt{3}\)

B. 450

C. \(225\sqrt{3}\)

D. 225

E. It cannot be determined from the information given.

Attachment:
2019-04-27_0141.png


PS19502.01
OG2020 NEW QUESTION

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In the floor plan of an executive's beach house above, the north and  [#permalink]

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New post 30 Apr 2019, 23:56

Solution



Image

Given:
Let us name the point in the diagram as shown.
    • AE = 30 ft
    • BE = 30 ft
    • CF = 15 ft
    • AD = 30 ft
    • CD = 30 ft

To Find:
    • Area of Bedroom or ∆ ACD

Approach and Working:

Since EF is parallel to BC, So, two corresponding angles of ∆ AEF and ∆ ABC will be equal.

    • ∆ AEF and ∆ ABC are similar triangles.
    • Therefore, \(\frac{AE}{AB}\) = \(\frac{AF}{AC}\)
    • \(\frac{30}{30 +30}\)= \(\frac{x}{x+15}\)
      o x = 15
      o AC = x+ 15 = 30 ft

    • Hence, ∆ ACD is an equilateral triangle since all the sides are equal.
      o Thus, Area of ∆ACD = \(\frac{√3}{4} * 30^2\) = 225√3

Therefore, option C is the correct answer.

Correct Answer: Option C
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Re: In the floor plan of an executive's beach house above, the north and  [#permalink]

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New post 02 May 2019, 17:18
Bunuel wrote:
Image
In the floor plan of an executive's beach house above, the north and south walls of the living room are parallel. What is the floor area, in square feet, of the bedroom?


A. \(450\sqrt{3}\)

B. 450

C. \(225\sqrt{3}\)

D. 225

E. It cannot be determined from the information given.

Attachment:
2019-04-27_0141.png


PS19502.01
OG2020 NEW QUESTION


We see that a side of the smaller triangular kitchen is exactly half of the larger triangle that comprises of the bath, kitchen and living room (30 ft vs. 60 ft). Since the two triangles are similar, then the side of the kitchen that opens to the bedroom is 15 ft since the wall that borders the living room and the bedroom is 15 ft. Thus, the bedroom is in the shape of an equilateral triangle with side length of 30 ft. Therefore, the bedroom has an area of (30^2 x √3)/4 = 900√3/4 = 225√3 square feet.

Answer: C
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Re: In the floor plan of an executive's beach house above, the north and  [#permalink]

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New post 20 May 2019, 14:43
parallesim is what we need to pay attention in the beginning.
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Re: In the floor plan of an executive's beach house above, the north and  [#permalink]

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New post 20 May 2019, 18:00
Hi Scot/Payal,

What are we not subtracting the area of the "shark fin" portion? Response would be appreciated.
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In the floor plan of an executive's beach house above, the north and  [#permalink]

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New post 20 May 2019, 18:48
Bunuel wrote:
Image
In the floor plan of an executive's beach house above, the north and south walls of the living room are parallel. What is the floor area, in square feet, of the bedroom?


A. \(450\sqrt{3}\)

B. 450

C. \(225\sqrt{3}\)

D. 225

E. It cannot be determined from the information given.

Attachment:
2019-04-27_0141.png




PS19502.01
OG2020 NEW QUESTION



Mid point theorem, a line joining the mid point of two sides of a triangle is parallel and 1/2 the third side. Converse is also true.

Quora: https://www.quora.com/What-is-the-proof ... nt-theorem

So, the bedroom is basically an equilateral triangle with sides 30. Now we can easily find the area.
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In the floor plan of an executive's beach house above, the north and   [#permalink] 20 May 2019, 18:48
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