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Bunuel
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statement 1: insufficient
we need the length of the square

statement 2: insufficient
we do not know the height of the trapezoid (w) and therefore cannot figure out the are of it and we also don't know the length of the square

statement 1+2: insufficient
the only part missing for us to find the area of each piece is the length of the square and we do not have that

Answer E!
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Solution: 3ft=36in
Area= Length * Width - 2*Area of triangle having base and height as w = 36*w - 2*w*(w/2) ---- eq 1
To determine the area of each piece, we need to know the value of w:

Statement 1: w = 3 inches
Plugging the value of w in eq 1 we can get the area - Sufficient

Statement 2: PQ = \sqrt{18} inches
PQ is hypotenuse of Isosceles triangle with other sides as w.
w^2 + w^2 = PQ --> w=3
Plugging the value of w in eq 1 we can get the area - Sufficient

Each statement alone is sufficient, Answer D
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Bunuel

Tough and Tricky questions: Geometry.




The figure above shows the dimensions of a square picture frame that was constructed using four pieces of frame as shown. If w is the width of each piece of the frame, what is the area of each piece?

(1) w = 3 inches
(2) PQ = \(\sqrt{18}\) inches

Statement 1:
The following figure is yielded:


Since the frame is divided into 4 equal pieces, we get:
Each piece = \(\frac{(4-red-rectangles) + (4-blue-squares)}{4}\).
Thus, the area of each piece can be determined.
SUFFICIENT.

Statement 2:
In the figure for Statement 1, PQ = \(\frac{(diagonal-of-the-frame) - (diagonal-of-the-picture)}{2}\) = \(\frac{36√2 - 30√2}{2}\) = \(\frac{6√2}{2}\) = 3√2 = √18 inches.
Thus, Statement 2 implies the same figure as Statement 1.
Since Statement 1 is sufficient, so is Statement 2.
SUFFICIENT.

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vietnammba
I think the answer is D.

Area of each piece S= (3ft*3ft-(3f-w)*(3ft-w))/4
Statement 1: w=3inch => we can calculate S. Suff
Statement 2: We know PQ and PQ is hypotenuse of a right isolece triangle w, we can calculate w => we can calculate S. Suff

The highlighted should be (3f-2w)
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Bunuel

The figure above shows the dimensions of a square picture frame that was constructed using four pieces of frame as shown. If w is the width of each piece of the frame, what is the area of each piece?

(1) w = 3 inches
(2) PQ = \(\sqrt{18}\) inches


DS87602.01

Attachment:
2007-01-02_114321_z.jpg

Bunuel The below highlighted part in the question is left out. Requesting you to add the same.
The figure above shows the dimensions of a square picture frame that was constructed using four identical pieces of frame as shown. If w is the width of each piece of the frame, what is the area of the front surface of each piece? (1 ft = 12 inches)
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Bunuel

The figure above shows the dimensions of a square picture frame that was constructed using four pieces of frame as shown. If w is the width of each piece of the frame, what is the area of each piece?

(1) w = 3 inches
(2) PQ = \(\sqrt{18}\) inches


DS87602.01

Attachment:
2007-01-02_114321_z.jpg

Bunuel The below highlighted part in the question is left out. Requesting you to add the same.
The figure above shows the dimensions of a square picture frame that was constructed using four identical pieces of frame as shown. If w is the width of each piece of the frame, what is the area of the front surface of each piece? (1 ft = 12 inches)

__________________
Fixed. Thank you.
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IMO :- D

Area of Frame is Trapezium

Area is Only dependent on "w"

1) W is given - Sufficient

2) PQ is given, PQ= Sqrt(2) * w - Sufficient
Attachments

Solution.jpg
Solution.jpg [ 2.67 MiB | Viewed 15370 times ]

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yashikaaggarwal
Bunuel Sir, can you also post the official explanation? I still didn't get what the question is asking for total surface area or area of frame. Please.

Posted from my mobile device

PFA the OFFICIAL EXPLANATION

IMO, TSA and area are the same for a 2D object.
Attachments

a1.JPG
a1.JPG [ 74.31 KiB | Viewed 15185 times ]

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Bunuel

The figure above shows the dimensions of a square picture frame that was constructed using four identical pieces of frame as shown. If w is the width of each piece of the frame, what is the area of the front surface of each piece? (1 ft = 12 inches)

(1) w = 3 inches
(2) PQ = \(\sqrt{18}\) inches


DS87602.01

Attachment:
The attachment 2007-01-02_114321_z.jpg is no longer available


Superb question. Please find attached the explanation for the question.

Answer D
Attachments

c825773b-0b22-4ef2-9a8f-9006bf6effeb.jpg
c825773b-0b22-4ef2-9a8f-9006bf6effeb.jpg [ 118.17 KiB | Viewed 14132 times ]

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Why is everyone assuming that sides of the inner square are parallel to the sides of the outer square? Could not the inner square be rotated within the outer square in different ways such that the four pieces of frame are still identical but the sides of the inner square are not parallel with those of the outer square? The problem does not state that they are parallel so we cannot assume it. It does not state that PQ bisects the right angle. I believe the answer should be E.

Example shown below:
Attachments

File comment: example
Untitled.jpg
Untitled.jpg [ 8.23 KiB | Viewed 13835 times ]

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mcolbert
Why is everyone assuming that sides of the inner square are parallel to the sides of the outer square? Could not the inner square be rotated within the outer square in different ways such that the four pieces of frame are still identical but the sides of the inner square are not parallel with those of the outer square? The problem does not state that they are parallel so we cannot assume it. It does not state that PQ bisects the right angle. I believe the answer should be E.

Example shown below:


In this case, how can you consider the width of each frame w?
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Bunuel

The figure above shows the dimensions of a square picture frame that was constructed using four identical pieces of frame as shown. If w is the width of each piece of the frame, what is the area of the front surface of each piece? (1 ft = 12 inches)

(1) w = 3 inches
(2) PQ = \(\sqrt{18}\) inches


DS87602.01

Attachment:
2007-01-02_114321_z.jpg

Bunuel I didn't understand why each angle will be 45 degrees for the trapezium. Can you please help me understand?
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