**44**

n- the number of cans, n>15

n=x^2+8, x- the size of square

n+11= y*(y+6), y- the width of the rectangle

Let's try some numbers of x to find y

For x=3/4/5/6 we get n+11=28/35/44/55

By solving y^2+6y-(n+11)=0 for each value of n+11 above we only get one integer solution (for n+11=55 only), therefore the solution is **n=44**, where 44=6^2+8 and 44=5*11-11