Answer/Step-by-step explanation:
Length of rectangle = [tex] l [/tex]
Width of rectangle = [tex] \frac{1}{3} of l - 1 = \frac{1}{3}l - 1 = \frac{l}{3} - 1 [/tex]
A. Expression for finding area of the rectangle:
Area of rectangle is given as [tex] length*width [/tex]
[tex] Area = l(\frac{l}{3} - 1) [/tex]
Or
[tex] Area = l*\frac{l}{3} - l*1 [/tex]
[tex] Area = \frac{l^2}{3} - l [/tex]
b. Expression for finding perimeter:
Perimeter of rectangle is given as [tex] 2(Length + Width) [/tex]
[tex] Perimeter = 2(l + (\frac{l}{3} - 1)) [/tex]
Or
[tex] Perimeter = 2(l) + 2(\frac{l}{3} - 1) [/tex]
[tex] Perimeter = 2l + \frac{2l}{3} - 2) [/tex]
c. Quotient of Perimeter divided by area:
[tex] 2(l + (\frac{l}{3} - 1)) [/tex] ÷ [tex] l(\frac{l}{3} - 1) [/tex]
[tex]2(l + (\frac{l}{3} - 1))[/tex] ÷ [tex]\frac{l^2 - 3l}{3}[/tex]
Change the ÷ to × and flip the fraction on your right upside down.
[tex]2(l + (\frac{l}{3} - 1)) * \frac{3}{l^2 - 3l}[/tex]
[tex]2l + 2(\frac{l}{3} - 1) * \frac{3}{l^2 - 3l}[/tex]
