Question

I need the answer.Help me out

Answer 1

The answer is $\boxed{7},$ where $a=5$ and $b=2.$

Solution sketch:

Apply the Pythagorean theorem to find $EC$ and $AE,$ which you then use to find $AD$ and $BC.$ Apply Heron's formula to $\triangle ABC$ to find that its area is 10, and then use $[ABC]=\frac{(AB)(CF)}{2}$ (base times height over 2) to finish by solving for $CF.$.