F(x) = x^2. What is g(x)?

In triangle △abc, ∠abc=90°, bh is an altitude. find the missing lengths. ah=4 and hc=1, find bh.

I’ve been trying all day to figure this puzzle out. i need the work for it aswell. it is a factoring polynomials tarsia. the image is below.

I’m really confused and need to learn this