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

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Math Expert
Joined: 02 Sep 2009
Posts: 60678
In the floor plan of an executive's beach house above, the north and  [#permalink]

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26 Apr 2019, 01:43
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Difficulty:

65% (hard)

Question Stats:

60% (02:24) correct 40% (02:32) wrong based on 724 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 [ 26.05 KiB | Viewed 8039 times ]

PS19502.01
OG2020 NEW QUESTION

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

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

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20 May 2019, 18:48
1
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

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.
ISB School Moderator
Joined: 08 Dec 2013
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Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB
GMAT 1: 630 Q47 V30
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Re: In the floor plan of an executive's beach house above, the north and  [#permalink]

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25 May 2019, 07:55
1
ankur_1988 wrote:
What are we not subtracting the area of the "shark fin" portion? Response would be appreciated.

[/quote]

I think those are doors.
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In the floor plan of an executive's beach house above, the north and  [#permalink]

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

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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3230
In the floor plan of an executive's beach house above, the north and  [#permalink]

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30 Apr 2019, 23:56

Solution

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

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

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02 May 2019, 17:18
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

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.

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

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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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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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25 May 2019, 07:48
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

ankur_1988 wrote:
Hi Scot/Payal,

What are we not subtracting the area of the "shark fin" portion? Response would be appreciated.

I think the answer should be E unless the Q clearly specifies that the "shark fin" is part of the bedroom. We wouldn't have cared about the area of "shark fin" if we had 2 "shark fins" connected to the bedroom, one outside and one inside so that they could have cancelled each other out.

From the tags, it seems to be an official Q but I'm surprised that an official Q has this kind of ambiguity.

Any thoughts on that? Thanks!
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Re: In the floor plan of an executive's beach house above, the north and  [#permalink]

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27 May 2019, 05:20
ankur_1988 wrote:
Hi Scot/Payal,

What are we not subtracting the area of the "shark fin" portion? Response would be appreciated.

The “shark fin” portions in the diagram tell us that there’s a door there and also tells us in which direction the door is opening. It’s the way technical drawings for floor plans are made. Considering also that we are told neither about the dimensions of the “shark fin” parts nor that those sections are actually quarter circles as they look, we can safely ignore those portions.
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# Scott Woodbury-Stewart

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Scott@TargetTestPrep.com
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Re: In the floor plan of an executive's beach house above, the north and  [#permalink]

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29 May 2019, 13:26
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

We can use mid point theorem. 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.

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Posts: 12
Re: In the floor plan of an executive's beach house above, the north and  [#permalink]

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30 May 2019, 14:58
EgmatQuantExpert wrote:

Solution

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

I dint know that they test 'similar triangles' on GMAT. Can you share how can we determine whether the two triangles are similar or not?
Re: In the floor plan of an executive's beach house above, the north and   [#permalink] 30 May 2019, 14:58
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