题目信息
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)
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
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正确答案：
D:EACH statement ALONE is sufficient.
Geometry Quadrilaterals; Area
Determine the area of the surface of each of the four pieces of wood used to construct the square picture frame. In the following explanation, the larger square with one vertex labeled P will be referred to as Square P and the smaller square with one vertex labeled Q will be referred to as Square Q.
It is given that the width of each piece of wood is 3 inches. Then, the area one piece of wood, in square inches, is
or 
; SUFFICIENT.
It is given that PQ = 
= 
inches. Since the pieces of the frame are identical, each of the angles at P is 45° and ΔPRQ in the figure above is a 45°−45°−90° triangle. It follows that RQ = 3. This is the same information given in (1), which was shown to be sufficient; SUFFICIENT.
The correct answer is D;each statement alone is sufficient.
Determine the area of the surface of each of the four pieces of wood used to construct the square picture frame. In the following explanation, the larger square with one vertex labeled P will be referred to as Square P and the smaller square with one vertex labeled Q will be referred to as Square Q.
It is given that the width of each piece of wood is 3 inches. Then, the area one piece of wood, in square inches, is
or ; SUFFICIENT.
It is given that PQ = = inches. Since the pieces of the frame are identical, each of the angles at P is 45° and ΔPRQ in the figure above is a 45°−45°−90° triangle. It follows that RQ = 3. This is the same information given in (1), which was shown to be sufficient; SUFFICIENT.The correct answer is D;each statement alone is sufficient.
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