题目信息
In rectangular region PQRS above, T is a point on side PS. If PS = 4, what is the area of region PQRS ?
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.
参考答案及共享解析
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已选答案：
正确答案：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Geometry Triangles
It is given that PQRS is a rectangle and PS = 4. The area of PQRS can be determined if and only if PQ can be determined.
It is given that ΔQTR is equilateral. If 
is the height of ΔQTR as shown above, then ΔQUT is a 30−60−90° triangle with UR = 2. Using the ratios for 30−60−90 triangles, TU = 
. Since PQ = TU, the area of PQRS can be determined; SUFFICIENT.
Given that PT = TS, PQ could be any positive number. Thus, it is not possible to determine PQ and therefore not possible to determine the area of PQRS; NOT sufficient.
The correct answer is A;statement 1 alone is sufficient.
It is given that PQRS is a rectangle and PS = 4. The area of PQRS can be determined if and only if PQ can be determined.
It is given that ΔQTR is equilateral. If is the height of ΔQTR as shown above, then ΔQUT is a 30−60−90° triangle with UR = 2. Using the ratios for 30−60−90 triangles, TU = . Since PQ = TU, the area of PQRS can be determined; SUFFICIENT.
Given that PT = TS, PQ could be any positive number. Thus, it is not possible to determine PQ and therefore not possible to determine the area of PQRS; NOT sufficient.The correct answer is A;statement 1 alone is sufficient.
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