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: $\frac{(x+4)(x+1)}{x+2}$

Step-by-step 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 $h$:

$h=\frac{x^{2}+5x+4}{(x+2)}$

Factoring in the numerator:

$h=\frac{(x+4)(x+1)}{x+2}$ This is the length of the other side of the rectangle