Krishna
0

Step 1: Make a note of the known and unknown measurements


Step 2: Represents the given relation between height and base through variables.

            NOTE: height (h) is 4 units shorter than its base

                          h = b - 4  


Step 3: Set up a formula of area of isosceles triangle to write 

            FORMULAS:

              Area of an isosceles triangle = \frac{1}{2} b*h

              Where b - base and h - height (altitude)

                   h (Altitude) = \sqrt{a^2 - \frac{b^2}{4}}


Step 4: Substitute the known values in the area formula.

            

            EXAMPLE:  Area of an isosceles triangle = \frac{1}{2} b*h

                                              30 = [math]\frac{1}{2}\ \left[b\ \left(b\ -\ 4\right)\right]\ [/math]


Step 5: Simplify the equation to find the unknown value (base)

              EXAMPLE :   60 = b^2 - 4b   

                                    b^2-4b-60=0

                     Solve the quadratic equation

                         b^2 - 10b + 6b - 60 = 0

                                      b(b - 10) + 6 (b - 10) = 0

                                      (b - 10)(b + 6) = 0

               Solutions to the equation: b = 10 and b = - 6 

                b is a length and therefore is positive b = 10 


Step 6: Find the height of the triangle by plugging the base values in the relation

              EXAMPLE;  h = b -4

                                  h = 10 - 4 = 6


Step 7:  Set up a formula to calculate the lateral side of an isosceles triangle.


            NOTE: Isosceles triangle is a combination of two right triangle.

                          Pythagoras theorem

          FORMULA: (lateral\ side)^2=(height)^2+\left(\frac{base}{2}\right)^2  


Step 8: Find the lateral side of an isosceles triangle.

            EXAMPLE: (lateral\ side)^2=6^2+(\frac{10}{2})^2

                                lateral\ side=\sqrt{36\ +\ 25}          

                                lateral\ side=\sqrt{61}