Answer:
Option 4 is correct
[tex]P=5+6w[/tex]
Step-by-step explanation:
Perimeter of a rectangle is given by:
[tex]P=2(l+w)[/tex] ....[1]
where w be the width of the rectangle and l be the length of the rectangle.
As per the statement:
length of a rectangle is 5/2 units greater than twice its width.
⇒ [tex]l = \frac{5}{2}+ 2w[/tex] units
Substitute this in [1] we get;
[tex]P=2(\frac{5}{2}+ 2w+w)[/tex]
Combine like terms;
[tex]P=2(\frac{5}{2}+3w)[/tex]
Using distributive property: [tex]a\cdot (b+c) =a\cdot b+ a\cdot c[/tex]
[tex]P=5+6w[/tex]
Therefore, the perimeter of the rectangle in terms of w is [tex]P=5+6w[/tex] units
