Question

a rectangle has an area of $k^{2}+19k + 60$ 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.

Explanation:

Step1: Factor the quadratic expression

We factor \(k^{2}+19k + 60\). We need to find two numbers that multiply to \(60\) and add up to \(19\). The numbers are \(15\) and \(4\). So, \(k^{2}+19k + 60=(k + 15)(k+4)\).

Answer:

The width of the rectangle is \(k + 4\) inches.