Please help me. What is the correct answer?

c. 12

Step-by-step explanation:

(BC)^2=(BD)^2+(DC)^2

thus

(BC)^2=h^2+16^2

hence combing the values for (BC)^2 we get:

25^2-(h^2+9^2)=h^2+16^2

simplifying we obtain:

625-h^2-81=h^2+256

putting like terms together

625-81-256=h^2+h^2

288=2h^2

thus

h^2=144

hence

h=√144

h=12 units

hope this helps :)