SOLUTION: 1. The triangle has an area of 2500 m2. The sides are in the ratio 5:10:11. Find the following a) Length of the longest side. b) Length of the median to the shortest side. c)

From the condition, the sides are a = 5x, b = 10x and c = 11x units long.


Apply the Heron's formula for the area of a triangle.


Semi-perimeter is  s =  = 13x.

                       s - a = 13x -  5x = 8x

                       s - b = 13x - 10x = 3x

                       s - c = 13x - 11x = 2x


According to the Heron's formula, the area of the triangle is


    area =  =  = .


So, the "area" equation to find x is


     = 2500.


From the equation,  x^2 = ;    x = .


Hence, the sides are  a =  5x = ;  

                      b = 10x = ;

                      c = 11x = .


The longest side is c = 11x = .      <<<---===  It is the ANSWER to question (a).


Find the altitude   drawn to this side from the area equation


      = 2500,  


which gives  


      =  = .      <<<---===  It is the ANSWER to question (c).



The radius of the incircle (inscribed circle) is

    r =  =  =  = .      <<<---===  It is the ANSWER to question (d).


The radius of the circumscribed circle is

    R = ,


and you just have EVERYTHING from me to complete this calculation ON YOUR OWN.