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
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