a rectangle has an area of $k^{2}+19k + 60$ square inches. if the value of k and the dimensions of the…

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?\nthe length of the rectangle is $k - 5$ inches.\nthe width of the rectangle is $k + 4$ inches.\nthe length of the rectangle is $k - 20$ inches.\nthe width of the rectangle is $k + 10$ inches.

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?\nthe length of the rectangle is $k - 5$ inches.\nthe width of the rectangle is $k + 4$ inches.\nthe length of the rectangle is $k - 20$ inches.\nthe width of the rectangle is $k + 10$ inches.

Answer

Explanation:

Step1: Factor the area 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)).

Step2: Analyze the options

Since the area of a rectangle (A = lw) and (A=(k + 15)(k + 4)), the possible length and width are (k + 15) and (k+4). Among the given options, the width of the rectangle could be (k + 4) inches.

Answer:

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