Problem of the Week

Problem E

The Area of the Year

In the diagram, $$\triangle AB_1C_1$$ is right-angled with $$AB_1=2$$ and $$AC_1=5$$. Lines $$AB_1$$ and $$AC_1$$ are extended and many more points are labelled at intervals of 1 unit, so that
$B_1B_2=B_2B_3=B_3B_4=B_4B_5=\ \cdots\ =1,\ \text{and}$
$C_1C_2=C_2C_3=C_3C_4=C_4C_5=\ \cdots\ =1.$
In fact, $$B_1B_j=j-1$$ and $$C_1C_k=k-1$$ for any positive integers $$j$$ and $$k$$.
For example, $$B_1B_{5}=5-1=4$$ and $$C_1C_{4}=4-1=3$$.
Determine the value of $$n$$ so that the area of quadrilateral $$B_nB_{n+1}C_{n+1}C_n$$ is 2020. That is, determine the value of $$n$$ so that the area of the quadrilateral with vertices $$B_n$$, $$B_{n+1}$$, $$C_{n+1}$$, and $$C_n$$ is 2020.