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? A- The length of the rectangle is k – 5 inches. B- The width of the rectangle is k + 4 inches. C- The length of the rectangle is k – 20 inches. D- The width of the rectangle is k + 10 inches.

Answer 1

Answer:

The correct statement is option (B)

The width of the rectangle is K+4 inches.

Step-by-step explanation:

Given that the area of a rectangle is

K²+19k+60

=k²+15k+4k+60

=k(k+15)+4(k+15)

=(k+15)(k+4)

We know that the area of rectangle is = length ×width

Therefore

K²+19k+60 =length ×width

⇒(k+15)(k+4)=length ×width

∴Length =(k+15) inches and width = (k+4)inches

Therefore the length of the rectangle is (k+15)inches and width is (k+4) inches