ISOSCELES TRIANGLES rational isosceles triangle with altitude 8 are (10,10, 12). Rational Scalene Triangles: Brahmagupta lays down the following rule in the case of rational scalene triangle; In other words, if m, p. q are any rational numbers, then the sides of a rational scalene triangle are: The square of an optional number is divided twice by two arbitrary numbers; the moieties of the sums of the quotients and (respective) optional numbers are the sides of a scalene triangle; the sum of the moities of the differences is the base.¹ B 'm² + (™² +p ), ³ (²+² +9). H ² ² (™²- -- p) + ÷ (~ / ² − a ) p Here the altitude (m), area and segments of the base of this triangle are all rational. Thus putting m=12, p=6, and q-8 in Brahmagupta's gene ral equation, Prthudaka Svam derives a scalene triangle with sides (13,15) and (14) altitude (12). area (84 and the segments of the base (5) which are all integral numbers. + (1 - ² + p) = 1 (² ²*+6)=15; 263 12² ÷ (m² +9)= 7 (¹²8² +8 ) −13 C' A' B' CH Fig. 19 1. इष्टद्रयेन भक्तो द्विषेष्ट वर्ग फलेष्टयोगायें। विषमत्रिभुजस्य भुजाविष्टोनफलायोगोभूः || B Fig. 20 -BrSpSi. XII, 34.
