Question

the area of a rectangle is given by the expression x^2+5x+4. If the length of one side is given by x+2, what is the length of the other side?

Answer 1

Answer:
`((x+4)(x+1))/(x+2)`

Explanation:

The area of a rectangle
`A` is given by the multiplication of its base
`b` by its height
`h`:

`A=(b)(h)=x^(2)+5x+4` (1)

In addition we are told the length of one of the sides (let's choose
`b`) is:

`b=x+2` (2)

Substituting (2) in (1):

`(x+2)h=x^(2)+5x+4` (3)

Isolating
`h`:

`h=(x^(2)+5x+4)/((x+2))`

Factoring in the numerator:

`h=((x+4)(x+1))/(x+2)` This is the length of the other side of the rectangle