Drawing a diagram I saw that EH = FG so 2x=x+3, and x=3.
I felt this was a bit too simple, though, so is it correct?
+506 Your instinct was correct: EG isn't necessarily equal to FG.
Here's a solution:
Notice that DGH and DFE are similar. We can set up an equation:
x−4x−7=(x−4)+2x(x−7)+(x+3)x−4x−7=3x−42x−4(x−4)(2x−4)=(x−7)(3x−4)2x2−12x+16=3x2−25x+280=x2−13x+12(x−12)(x−1)=0x=1,x=12
1 is extraneous because it will be negative for x-4, which is impossible.
Therefore the answer is 24
