Asked by Anonymous
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?
Answers
Answered by
Damon
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
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
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