HELP PLEASE! Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.A. 8 in.B. 11.3 in.C. 8.5 in.D. 6.2 in.

Answer:Option C. 8.5 in.Step-by-step explanation:see the attached figure with letters to better understand the problemwe know thatThe formula of area of triangle is equal to[tex]A=\frac{1}{2}(b)(h)[/tex]In this problemwe have[tex]b=BC=6\ in[/tex][tex]h=AD=x\ in[/tex]substitute[tex]A=\frac{1}{2}(6)(x)[/tex][tex]A=3x\ in^{2}[/tex] ------> equation 1Remember that Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  Let  a,b,c be the lengths of the sides of a triangle.  The area is given by: [tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex] where p is half the perimeter p=[tex]\frac{a+b+c}{2}[/tex] we have [tex]a=9\ in[/tex] [tex]b=9\ in[/tex] [tex]c=6\ in[/tex] Find the half perimeter p p=[tex]\frac{9+9+6}{2}=12\ in[/tex] Find the area [tex]A=\sqrt{12(12-9)(12-9)(12-6)}[/tex] [tex]A=\sqrt{12(3)(3)(6)}[/tex] [tex]A=\sqrt{648}[/tex] [tex]A=25.46\ in^{2}[/tex] Substitute the value of the area in the equation 1 and solve for x[tex]A=3x\ in^{2}[/tex] [tex]25.46=3x[/tex] [tex]x=25.46/3[/tex] [tex]x=8.5\ in[/tex]