Question

Look at the figure find the value of x. 4x-16 2x-4 3x-2

Answer 1

From the given figure we can write , using Pythagoras theorem

$\\ \ BG^2=GC^2+BC^2\\ \\ BG^2=GA^2+AB^2\\ \\ \Rightarrow GC^2+BC^2=GA^2+AB^2\\ \\ \ \Rightarrow (4x-16)^2+(3x-2)^2=(2x-4)^2+(3x-2)^2\\ \\ \ \Rightarrow (4x-16)^2=(2x-4)^2\\ \\ \Rightarrow (4x-16)=(2x-4)\Rightarrow 4x-2x=16-4\\ \\ \ \Rightarrow 2x=12\Rightarrow x=6$