triangles

 

A triangle has integer side lengths 2, 5 and x. What is the area of the triangle if x = 6?     

 

I think it'd be easier to go with Heron's Formula than trying to manipulate trig functions.     

 

        s  =  ¹/₂ • (a+b+c)     

        s  =  ¹/₂ • (2 + 5 + 6)  =  6.5     

 

        A  =  sqrt ( (s)(s–a)(s–b)(s–c) )     

        A  =  sqrt ( 6.5 • 4.5 • 1.5 • 0.5 )     

        A  =  sqrt ( 65.8125 )     

        A  =  8.1125     (as a fraction, 8 ⁹/₈₀ )     

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