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CHAPTER VI-MEASUREMENT OF AREAS. 236 the optionally ollosen quantity gives rise to the measure of the perpendicular,
An example in illustration thereof.
157}. In the case of an isosceles triangular figure, the accurate measurement of the area is 12. The optionally chosen quantity is 3. Give out quickly, O friend, the values of (its) sides, base, and perpendicular.
The rule for arriving, aftor knowing the exact numorical measure of a (given) area, at a triangular figure with upoqual sides, having that same accurately measured area (as its own) :--
1581. The giveu area is multiplied by eight, and to the rosulting produot the square of the optionally chosen quantity is added. Then the square root (of the sum so resulting is obtainod). The cube (of this square root) is (thereafter) divided by the optionally chosen number and (also) by the square root (obtained as abovo). Half of the optionally chosen number gives the measure of the base (of the required triangle). The quotiont (obtained in the previous operation) is lessened (in valne) by tho (measuro of this) base. The resulting quantity) is to be used in carrying out the sankramana process in relation to the egnaro of the optionally chosen quantity as divided by two as woll as the square root (mentioned above). (Thuy) the values of the sides arc arrived at.
1584. If A represents the area of & triangle, and in the optionally chosen number, then according to the rule the required values are obtainod than :
2 -- bago; (W8A+dad
& N 8A+H 2 3 N 8A + d' = siden. and
2 When the area and the base of a triangle arc kiven, tbo locos of the vertor is a lino parallel to the bano, and the sides can have any met of valoon. In onder to arrive at spuoifc set of values for the siden, it is evidently msumod here that the sum of the two sides is equal to the sum of the base and twise the altitudo, 6..., equal to +24. With this serumption, the formula nbove
"2d24 given for the measure of the sides can be derived from the general formula for the area of the triangle, Nele-a) ( b) ( c) given in apzs 60 of this chapter.
