History of Hindu Mathematics: A Source Book v2.c17.s18.t2.70

v2.c17.s18.t2.70

Now, juxtaposing these two rectangles so that they do not overlap (Fig. 3), the sides of the rational scalene triangle are obtained as $p² + q², m² + n², (p² - q²) + (m² - n²),$ where mn = pq. Evidently the two rectangles can be juxtaposed so as to overlap (Fig. 4). So the general solution will be $p² + q², m² + n², (p² - q²) ± (m² - n²).$ The altitude of the rational scalene triangle thus obtained is 2mn or 2pq, its area pq(p² - q²) ± mn(m² - n²) and the segments of the base are p² - q² and m² - n².