Official Guide Explanation:
Problem Solving #157




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Solution and Metadata

Question: 157
Page: 83
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Triangles > Length of sides

Explanation: Given that it is a right triangle, we know that the two legs--that is, the two shortest sides, since the hypotenuse must be the longest--are the base and height. Thus, we're dealing with b and h in the formula

1 = (1/2)bh

2 = bh

If base and height were equal, each one would be rt[2]. However, we're looking for the larger of the two legs, the side that is the middle length of the three sides. So y must be greater than rt[2] and up to infinity. (The triangle could be very, very skinny.) Because there's no reason y can't be very large, look for the biggest choice. In this case, it's (A): y> rt[2].

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