Question

The area of a rectangle is 30+12x what are 3 possibilities for the length and width of the rectangle

Answer 1

In order to find the three possibilities, you must first think of common factors between 30 and 12:

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Factors of 12: 1, 2, 3, 4, 6, 12

We can find three common factors between the two numbers: 2, 3, and 6. So these are three widths that we can use. The length can be found by factoring out the numbers from 30+12x (we can't factor out x):

30+12x=2(15+6x)      Width: 2      Length: 15+6x

20+12x=3(10+4x)      Width: 3      Length: 10+4x

20+12x=6(5+2x)       Width: 6      Length: 5+2x