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jmc

geometry junior

Problem

In the figure below, side of rectangle is parallel to the -axis, and side contains the point . The vertices of triangle are , and . What is the ratio of the area of triangle to the area of rectangle ? Express your answer as a common fraction.

problem
Solution
The area of the triangle can be expressed as , where is the height of the triangle from C to AE. However, the rectangle's area can be expressed as AE, since AB DE , thus, the ratio of the triangle's area to the rectangle's is .
Final answer
\frac{1}{2}