Triangle ABC is isosceles with AB = BC If AC = 20 and [ABC] = 240, then find the perimeter of triangle ABC.
I think it's maybe Heron's Formula? I've been trying it but I keep getting confused with all the square roots and everyone is giving me different answers. I don't know hich one to trust. Any help would be AMAZING and will mean a WHOLE LOT to me.
Area of triangle =[Base x Height ]/ 2
240 = [20 x Height] / 2
Height =480 / 20
Height = 24
Draw a perpendicular line to AC
AC/2 =10 - This divides the triangle into 2 congruent triangles.
The height of each of these 2 triangles =24 and the base of each =10
Using Pythagoras's Theorem:
24^2 + 10^2 =AB^2 =BC^2
AB^2 =576 + 100 =676 Take the sqrt of both sides
AB = 26 = BC
The perimeter =26 + 26 + 20 = 72
