2021 Cayley Problem 25

The points J(2,7), K(5,3) and L(r,t) form a triangle whose area is less than or equal to 10. Let \mathcal{R} be the region formed by all such points L with 0 \le r \le 10 and 0 \le t \le 10. When written as a fraction in lowest terms, the area of \mathcal{R} is equal to \dfrac{300 + a}{40 - b} for some positive integers a and b. The value of a + b is

\textbf{(A)}\ 82\quad \textbf{(B)}\ 71\quad \textbf{(C)}\ 60\quad \textbf{(D)}\ 49\quad \textbf{(E)}\ 93

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.