Question

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

The length of the rectangle is k – 5 inches.
The width of the rectangle is k + 4 inches.
The length of the rectangle is k – 20 inches.
The width of the rectangle is k + 10 inches.

Answer 1

k^2 + 19k + 60 = (k + 15)(k + 4).

So the rectangle’s sides can be k + 15 and k + 4 (both natural when k is natural). Hence "The width of the rectangle is k + 4 inches."