24 MATHEMATICS 



The area of any triangle may be found by means of the 

 following formula, in which A the area, and a, b, and c 

 represent the lengths of the sides: 



EXAMPLE. What is the area of a triangle whose sides are 

 21 ft., 46 ft., and 50 ft. long? 



SOLUTION. In order to apply the formula, assume that 

 a represents the side that is 21 ft. long; b, the side that is 50 ft. 

 long; and c, the side that is 46 ft. long. Then substituting 

 in the formula, 



'212 + 502-462\2 



26/2 \ V 2X50 



50 ^ / 



68.0625 = 25 A/372.9375 

 = 25X19.312 = 482.8 sq. ft., nearly 



The above operations have been extended much further 

 than was necessary in order to show every step of the process. 

 The Rankine-Gordon formula for determining the least 

 load in pounds that will cause a long column to break is 



in which P = load (pressure)in pounds; S = ultimate strength, 

 in pounds per square inch, of material composing column; 

 A = area of cross-section of column, in square inches; q = a. 

 factor (multiplier) whose value depends on the shape of the 

 ends of the column and on the material composing the column ; 

 / = length of the column, in inches; G = least radius of gyration 

 of cross-section of column. 



The meaning of the term G is explained on page 142. 



EXAMPLE. What is the least load that will break a hollow 

 steel column whose outside diameter is 14 in., inside diam- 

 eter 11 in., length 20 ft., and whose ends are flat? 



SOLUTION. For steel, 5 = 150,000, and g= for flat- 



