Krishna
0

Step 1: Make a note of the given data

             NOTE:  Triangle perimeter = 60

                           Triangle area  = 150 units^2

                          Find the  sides measurements


Step 2: Draw an imaginary figure and set up an equation from the given data

                

                  Triangle perimeter = 60

                    a + b + h = 60 ........................(1)

                   Triangle area  = 150 units^2

                             \frac{1}{2}(a*b) = 150 unit^2                  

                          ab = 300 ............................(2)


Step 3: Solve the equations (1)

             a + b + h = 60

                 Skill 1: Rewrite the equation

                             as follows 

                                a + b = 60 - h 

                 Skill 2:   Square both sides 

                               (a + b)2 = (60 - h)2

                 Skill 3:   Expand both sides 

                           a^2 + b^2 + 2 a b = 60^2 + h^2 - 120 h

                 Skill 4:  Combine the equation a^2 + b^2 = h^2

                                with the above equation to obtain 

                         2 a b = 60^2 - 120 h 

                 Skill 5: a b is known to be equal to 300, hence the above

                             equation  becomes 

               600 = 60^2 - 120 h

                Skill 6: Solve for h to obtain 

                           h = 25 units 


Step 4: Substitute h by 25 in the equation a + b + h = 60

                 a + b = 60 - 25 = 35 

          


Step 5:  a b = 300, then [math] b = \frac{300}{a} which is substituted in the

               equation a + b = 35


                 a + \frac{300}{a -35} = 0


Step 5 : Do the L.C.M to obtain a quadratic equation of the form 

               a^2 - 35a + 300 =0


Step 6: Solve the above equation to obtain two solutions 

                a = 20 and a = 15 


            The two sides of the right triangle and the hypotenuse are,

             respectively, given by 

                   15 units, 20 units and 25 units. 

       If you want you can check the perimeter and area given in the problem.