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  3. If the lengths of the legs of a right triangle are integers, what is the area of the triangular region? (1) The length of one le

If the lengths of the legs of a right triangle are integers, what is the area of the triangular region? (1) The length of one le

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问题 If the lengths of the legs of a right triangle are integers, what is the area of the triangular region?
(1) The length of one leg is  3/4 the length of the other.
(2) The length of the hypotenuse is 5.
选项 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.
答案B
解析 (1)    Let x represent one leg of the triangle. Then the other lee is  3x/4 and the area is 3x2/8. Since the value of x can be any positive multiple of 4, the area cannot be determined; NOT sufficient.
(2)    Given that the lengths of the legs are the integers a and b and the length of the hypotenuse is 5, it follows that a 2 + b 2 = 25, where 1 ≤ a ≤ 4 and 1 ≤ b ≤ 4. The only pair of integers that meet these conditions are 3 and 4, so the area of the triangular region is 6; SUFFICIENT.
The correct answer is B; statement 2 alone is sufficient.
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