Bryan has 180 feet of fencing. he use the wall for one side of fencing
So he has to fence only 3 sides
he has to fence bottom side + left side+ right side of the wall
Let x be the width of the garden
Let y be the length
Perimeter of the garden = length + width + width
180 = y +x +x
180 = y+2x
so y = 180 - 2x
(a) Area of rectangle = Length * width
Area = y * x
Area = (180 -2x)* x
so area of the garden = -2x^2 +180x
(b)To find dimension to create largest are we find x coordinate of the vertex
formula is [tex]x= \frac{-b}{2a}[/tex]
a= -2 and b = +180
[tex]x= \frac{-180}{2(-2)}= 45[/tex]
So width = 45
We know length y = 180 - 2x= 180 - 2(45) = 90
Dimension with greatest area is
Length = 90 feet
width = 45 feet
(c) Greatest area = length * width
= 90 * 45 = 4050 square feet
