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

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

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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√3
B) 450
C) 225√3
D) 225
E) It cannot be determined from the information given.

C

Source: Official Guide 2020

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Let's set aside the fact that this is an awful floorplan. How would you find furniture to fit this house?!

If the two wall of the living room are parallel, then the kitchen and the (kitchen + living room + bath) are SIMILAR triangles. Similar triangles always have PROPORTIONAL sides. If we're given that the length of the left side of the kitchen is 30, and left side of the (kitchen + living room + bath) is 60 total, then the ratio of little triangle to big = 1 : 2. Thus, we can infer that the side lengths of the right-hand walls are 15 and 30:



If that's the case, then the bedroom (again, a ridiculously shaped room) is an EQUILATERAL triangle of 30 : 30 : 30.

To find the area of any equilateral triangle, chop it into two 30-60-90 triangles.


If the base is 30, the height will be $$15\sqrt{3}$$
So, (1/2)(base)(height) = $$\left(\frac{1}{2}\right)\left(30\right)\left(15\sqrt{3}\right)$$
$$=225\sqrt{3}$$

The answer is C.

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Harvard Graduate School of Education


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AbeNeedsAnswers 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√3
B) 450
C) 225√3
D) 225
E) It cannot be determined from the information given.

C

Source: Official Guide 2020
We see that a side of the smaller triangular kitchen is exactly half of the larger triangle that comprises 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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Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



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