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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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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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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]
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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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.
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In the floor plan of an executive's beach house above, the north and [#permalink]
1
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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]
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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Re: In the floor plan of an executive's beach house above, the north and [#permalink]
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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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Re: In the floor plan of an executive's beach house above, the north and [#permalink]
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This is the most screwed-up floor plan one could imagine! Why on Earth would you put a door between the kitchen and the bedroom??! Plus good luck with the bed in that triangular bedroom!
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In the floor plan of an executive's beach house above, the north and [#permalink]
@experts could you explain how we used the midpoint theorem here? :$how do we know that the north wall is cutting the bedroom side wall at the mid point ? CEO Joined: 07 Mar 2019 Posts: 2624 Own Kudos [?]: 1870 [1] Given Kudos: 763 Location: India WE:Sales (Energy and Utilities) In the floor plan of an executive's beach house above, the north and [#permalink] 1 Kudos Kritisood wrote: @experts could you explain how we used the midpoint theorem here? :$ how do we know that the north wall is cutting the bedroom side wall at the mid point ?

Kritisood
Please refer ShukhratJon's Solution for your answer.(According to the mid-point theorem, the line joining the mid-points of two sides of a triangle is parallel to the third side of the triangle. However, note that we are given that line DE is || to AC and lengths of AD = DB = 30. So, we have to apply the concept in a reverse manner.)

But i think you can solve the question without applying the similar triangles/midpoint theorem/concept.
Consider the rough diagram below. Consider the triangle △BCF. CE = 15, BF = CF = 30
Attachment:

Screenshot .png [ 23.65 KiB | Viewed 32532 times ]

Now if ∠ECF = 60° and on joining EF where EF⟂BC, we have right △FEC with ∠EFC = 30°. However, this has to be proved.(Note that this is about applying reverse concept and its a little time consuming.)

In a 30-60-90 right triangle the ratio of sides is $$x:\sqrt{3}x:2x$$.
Here, if △BCF is a 30-60-90 right triangle, then sides ratio is CE:EF:CF = 15:EF:30.
Thus, $$EF = 15\sqrt{3}$$
Therefore, with this logic you can prove BE(△BEF) = 15, implying △BCF is an equilateral triangle with side length of 30.

From here onwards the area of an equilateral triangle = $$\frac{\sqrt{3}}{4}*x^2$$ where x is the side of the triangle.
Area = $$\frac{\sqrt{3}}{4}*30^2$$
= $$225\sqrt{3}$$

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

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

A line drawn from the mid-point of one side of a triangle to the mid-point of the opposite side of the triangle will be:

(1)parallel to the third, parallel side

And

(2)Half the length of that third, parallel side

This means that the Unknown Distance to complete the 3rd side of the Bedroom is 15

Equilateral triangle with side length 30

Area = (30)^2 * sqrt(3) * (1/4) =

225 * sqrt(3)

Posted from my mobile device
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In the floor plan of an executive's beach house above, the north and [#permalink]
How we actually know that a combination of Bathroom Kitchen and Living room will be a triangle. The question doesn't tell us that a side of Bathroom and Kitchen is on the same line.
How can we assume that a combination of Bathroom Kitchen and Living room is a triangle
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Re: In the floor plan of an executive's beach house above, the north and [#permalink]
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: In the floor plan of an executive's beach house above, the north and [#permalink]
But what if the south wall of the bath is not in the same horizontal line as the south wall of the living room?
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Re: In the floor plan of an executive's beach house above, the north and [#permalink]
panpan19 wrote:
But what if the south wall of the bath is not in the same horizontal line as the south wall of the living room?

If a line looks like a line, it’s a line. panpan19

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