Question

In triangle ABC, the line BD is perpendicular to AC.
AD = (x + 6) cm, DC = (x + 2) cm and the height BD = (x + 1) cm.
(i) Find area of triangle in term of "X"​

Answer 1

S = A+B+C by 2  

 = (x+6)+(x+2)+(x+1) by 2

 =3x+ 9 by 2

Area=  √{s(s-a)(s-b)(s-c)},

         √{3x + 9 by 2 (3x+9 by 2 -( x+6))(3x+9 by 2 (- x+2))(3x+9 by 2 -(x+1))

         √{3x + 9 by 2 ( x+3 by 2 ) (x+5 by 2 ) ( x+6 by 2 )

          √{ 2 ( 3x + 9 ) (2(x + 3 )) (2(x+5)) (2(x+6))

            √{ (6x + 18 ) (2x - 6 ) (2x + 10) ( 2x + 12 )

             √{4x +  102

            2x + 51