Official Guide Explanation:
Problem Solving #85




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Solution and Metadata

Question: 85
Page: 72
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Coordinate Geometry > Other
Category 2: Geometry > Triangles > other

Explanation: The area of a triangle is (1/2)bh, and the base and height must be perpendicular. The base of this triangle is RT, so b is the distance between R and T, (1,0) and (c,0), respectively. Since c is the larger number (further to the right on the x - axis), the distance is c - 1, so b = c - 1. The height is a line parallel to the y - axis that you can draw between the x - axis and point S. That point on the x - axis has the coordinates (a,0). The distance between S and that point is b - 0, so h = b. (Note that we've used b in its conventional sense to stand for base, and also for the variable called b in this problem. Be careful, and realize that the GMAT does this on purpose!)

So, we can plug these values into the equation for area of a triangle: (1/2)(c - 1)(b) = ((b(c - 1))/2), choice (B).

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