The formula for the perimeter P of a rectangle with length L and width w is P = 2(L+W). Find the length of the rectangle shown here if the perimeter is 9 and 1/2 feet. Solve the equation for L and justify each step.

L = [tex]\frac{P - 2W}{2}[/tex] and L = 3 [tex]\frac{1}{2}[/tex]
distribute the bracket on the right side of the formula
P = 2L + 2W
subtract 2W from both sides
P - 2W = 2L
divide both sides by 2
L = [tex]\frac{P - 2W}{2}[/tex]
solve for L for P = [tex]\frac{19}{2}[/tex] and W = [tex]\frac{5}{4}[/tex]
L = ( [tex]\frac{19}{2}[/tex] - [tex]\frac{5}{2}[/tex])/2 = [tex]\frac{7}{2}[/tex] = 3 [tex]\frac{1}{2}[/tex]