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image.png

In the figure above, if the area of triangular region D is 4, what is the length of a side of square region A ?

1. The area of square region B is 9.

2. The area of square region C is image.png.


    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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答案:
D
Geometry Ar
ea
Let x be the length of a side of square region C and y be the length of a side of square region B. Then the area of triangular region D is image.pngxy and it is given that image.pngxy = 4, or xy =8. The Pythagorean theorem can be used to find the length of a side of square region A if the values of both x and y can be determined.
  1.  Given that the area of square region B is 9, it follows that y2 = 9, or y = 3. Since xy = 8, the value of x can be determined, and therefore the values of both x and y can be determined; SUFFICIENT.
  2. Given that the area of square region C is image.png, it follows that x2 = image.png, or x = image.png. Since xy= 8, the value of y can be determined, and therefore the values of both x and y can be determined; SUFFICIENT.


The correct answer is D; each statement alone is sufficient.


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