Arectangle has an area of k2+19k+60 square inches. if the value of k and the dimensions of the rectangle are all natural number, which statement about the rectangle could be true?

I assume you mean A = k^2 + 19k + 60. If the values of k are natural numbers then the area must be A = (k + 15)(k + 4) which is the factored form of the quadratic. The only statement about the rectangle that can be made is that the long side of the rectangle is 11 more than the short side. Lets say that k = 10 then the dimensions of the rectangle are 25 and 14.