Answer: [tex]\frac{(x+4)(x+1)}{x+2}[/tex]
Step-by-step explanation:
The area of a rectangle [tex]A[/tex] is given by the multiplication of its base [tex]b[/tex] by its height [tex]h[/tex]:
[tex]A=(b)(h)=x^{2}+5x+4[/tex] (1)
In addition we are told the length of one of the sides (let's choose [tex]b[/tex]) is:
[tex]b=x+2[/tex] (2)
Substituting (2) in (1):
[tex](x+2)h=x^{2}+5x+4[/tex] (3)
Isolating [tex]h[/tex]:
[tex]h=\frac{x^{2}+5x+4}{(x+2)}[/tex]
Factoring in the numerator:
[tex]h=\frac{(x+4)(x+1)}{x+2}[/tex] This is the length of the other side of the rectangle
