Question

Find the perimeter of a rectangle in simplest expression form that has an area of 6x2 +17x + 12 square feet. Be sure to include an explanation of why/how we factor the numbers.

Answer 1

To find the perimeter of a rectangle, we first need to factor the area expression to find the length and width. The given area is 6x^2 + 17x + 12. Let's factor this quadratic expression:

6x^2 + 17x + 12 can be factored as (2x + 3)(3x + 4), since (2x * 3x) = 6x^2, (2x * 4) + (3 * 3x) = 17x, and (3 * 4) = 12.

Now, we have the length and width of the rectangle: (2x + 3) and (3x + 4).

The perimeter of a rectangle is given by the formula P = 2L + 2W. Substitute the expressions for length and width:

P = 2(2x + 3) + 2(3x + 4)

Now, distribute the 2:

P = 4x + 6 + 6x + 8

Combine like terms:

P = 10x + 14

So, the perimeter of the rectangle is 10x + 14 feet in simplest expression form.