Answer: [tex]\frac{10}{r+5}[/tex]
The perimeter of a rectangle is given by the following formula:
[tex]P_{rectangle}=2w+2L[/tex] (1)
Where [tex]w[/tex] is the width of the rectangle and [tex]L[/tex] its length.
According to the image:
[tex]w=\frac{2}{r+5}[/tex] (2)
[tex]L=\frac{3}{r+5}[/tex] (3)
So, if we want to find an expression for the perimeter, we have to substitute equations (2) and (3) in (1):
[tex]P_{rectangle}=2(\frac{2}{r+5})+2(\frac{3}{r+5})[/tex] (4)
Solving and simplifying:
[tex]P_{rectangle}=\frac{10}{r+5}[/tex] >>>This is the expression
Therefore, the correct answer is option B.
