1984 AHSME Problem 17

A right triangle ABC with hypotenuse AB has side AC=15. Altitude CH divides AB into segments AH and HB, with HB=16. The area of \triangle ABC is

\mathrm{(A) \ }120 \qquad \mathrm{(B) \ }144 \qquad \mathrm{(C) \ } 150 \qquad \mathrm{(D) \ }216 \qquad \mathrm{(E) \ } 144\sqrt{5}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.