The length of a rectangle is 5/2 units greater than twice its width. If its width is w, which expression gives the perimeter of the rectangle in terms of w?1. 2(5/2w) + w2. 5/2w + w3. 3w + 10/24. 6w + 5

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] unitsSubstitute 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