Problem:
Two opposite sides of a rectangle are each divided into congruent segments, and the endpoints of one segment are joined to the center to form triangle . The other sides are each divided into congruent segments, and the endpoints of one of these segments are joined to the center to form triangle . [See figure for .] What is the ratio of the area of triangle to the area of triangle
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Solution:
Let the base of the rectangle be and the height . Triangle has an altitude of length to a base of length , and triangle has an altitude of length to a base of length . Thus the required ratio of areas is
