2. 外语
  3. BIn this question, you are asked to compare the area of triangle PQR with the area of triangle PSR. Note that both triangles are

BIn this question, you are asked to compare the area of triangle PQR with the area of triangle PSR. Note that both triangles are

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答案B
解析 In this question, you are asked to compare the area of triangle PQR with the area of triangle PSR. Note that both triangles are right triangles and that line segment PR is the hypotenuse of both triangles. Recall that the area of a triangle is equal to one-half the product of a base and the height corresponding to the base. Also, for any right triangle, the lengths of the two legs of the triangle are a base and the corresponding height.
   The area of triangle PQR: In the figure, it is given that the length of leg PQ isand the length of leg QR is. Therefore, you can conclude that the area of triangle PQR is, or 5.
   The area of triangle PSR: To calculate the area of triangle PSR, you need to know the lengths of the legs PS and RS. From the figure, you know that the length of RS is 3, but you do not know the length of PS. How can you determine the length of PS ? If, in addition to the length of RS, you knew the length of hypotenuse PR, you could use the Pythagorean theorem to determine the length of PS. So, to find the length of PS, you first need to find the length of hypotenuse PR.
   Recall that PR is also the hypotenuse of triangle PQR. The lengths of legs PQ and QR of triangle PQR areand, respectively. By the Pythagorean theorem,

Thus, the length of PR is, or 5.
   Returning to triangle PSR, you now know that the length of hypotenuse PR is 5 and the length of leg RS is 3. Therefore, by the Pythagorean theorem,
32 +(PS)2 = 52
9 +(PS)2 = 25
(PS)2 = 25-9
(RS)2 = 16
and the length of PS is 4.
   Since legs PS and RS have lengths 4 and 3, respectively, the area of triangle PSR is(4)(3), or 6. Recall that you have already determined that the area of triangle PQR is 5. So Quantity B, the area of triangle PSR, is greater than Quantity A, the area of triangle PQR, and the correct answer is Choice B.
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