A rectangle is to have a perimeter of 18m. the graph below shows the relationship between the area of the rectangle and its width. What is the width of the rectangle with the largest area?

1 answer

2 w + 2 L = 18
so
L = 9-w

A = w L = 9 w - w^2

w^2 - 9 w = -A
find vertex by completing the square for max A

w^2 - 9 w + (9/2)^2 = - (A-81/4)

(w -9/2)^2 = - (A-81/4)

w = 9/2 for max area

by the way that means 2 w = 9 and
therefore 2 L = 9 so it is a square with
sides = 9/2