Question

The area of a rectangular fountain is (x^2+12+20) square feet. A 2-foot walkway is built around the fountain. Find the dimensions of the outside border of the walkway

Answer 1

area=legnth times width
factor
what 2 numbes multiply to 20 and add to 12
10 and 2
(x+2)(x+10)

2 foot walkway is increase legnth and width by 2

area=LW
area=(x+2)(x+10)
increase each by 2
area=(x+4)(x+12)

the outside border is x+4 by x+12

Answer 2

`(x+14)*(x+6)` feet

Explanation:

We will start factorizing
`x^2+12x+20=(x+10)(x+2)`.

This factorization is telling us that the square fountain has dimensions:

Fountain Lenght=
`x+10` feet

Fountain Width=
`x+2` feet

Then, a 2 foot walkway is constructed around the fountain. Observe that this 2 foot need to be added in each of the 4 sides of the square fountain. So, the outer walkway dimensions are:

Outer walkway Lenght=
`x+14` feet

Outer walkway Width=
`x+6` feet