Krishna
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Step 1:  Assume common ratio is x

            NOTE: We know that there is a common ratio for all sides of the triangle.  

                            That means that if that common ratio is denoted as x

              

Step 2: Write the lengths of the triangle using the variable(x).

            EXAMPLE: Assume a = 3x, 4x, and 5x.


Step 3: Find the Area of the triangle

           Step 1: Calculate the semi perimeter of the triangle.

              NOTE: First calculate the perimeter of a triangle by adding up the length of  

               its three sides. Then, multiply by \frac {1}{2}


              EXAMPLE: \frac{1}{2} (a+b+c)

                                \frac{1}{2}(3x+4x+5x)

                                    s=\frac{1}{2}(12x)=6x


          Step 2: Substitute the values of semi perimeter and lengths of the triangle in

                      the area formula


             FORMULA: Area=\sqrt{s(s-a)(s-b)(s-c)},


            EXAMPLE:

            Area =\sqrt{6x(6x-3x)(6x-4x)(6x-5x)}


          Step 3: Calculate the values in parentheses.

                          EXAMPLE: [/math] \sqrt{6x(3x)(2x)(x)} [/math]

                                                                                        

          Step 4: Multiply the two values under the radical sign.Then, find their square  

                      root. 

                      EXAMPLE; = \sqrt{36 x^4}

                                        =   6x^2

Step 4: Equate the calculated area and the given area measurement

                       6x^2 = 216 cm^2

                       x^2 = \frac{216}{6} = 36

                       x = 6


Step 5: Find the real lengths of the triangle by substitute the x value in the assumed lengths.

              EXAMPLE:  3x = 3(6) = 18

                                    4x = 4 (6) = 24

                                    5x = 5 (6) = 30

Step 6:  Add all the lengths to know the perimeter of the circle

                Perimeter = 18 + 24 + 30 = 72 cm

      Therefore the pereimeter of the triangle = 72 cm