Answer:
Suppose you want to frame a collage of pictures. You have a 9-ft strip of wood for the frame. What dimensions of the frame give you the maximum area for the collage? What is the maximum area?
A:
Perimeter = 2(L + W) 9 = 2(L+W) L+W = 4.5 L = 4.5-W Area = LW Area = (4.5-W)W A = 4.5W - W^2 You have a quadratic with a = -1 and b = 4.5 Maximum area occurs when W = -b/(2a) = 4.5/(2*-1) = 2.25
Step-by-step explanation:
Dimension of the picture with 9ft strip of wood is
length = 2.25 ft and width =2.25 ft
Given :
you want to frame a collage of picture with a 9ft strip of wood.
the perimeter of the frame is 9 ft
Perimeter of rectangle = 2(length +width )
Let 'l' be the length and 'w' be the width
[tex]Perimeter =2(l+w)\\9=2(l+w)\\Divide \; by \; 2\\l+w=4.5\\l=4.5-w[/tex]
Now we find the area
[tex]Area = length \cdot width \\Area= l \cdot w\\A= (4.5-w)(w)\\A=-w^2+4.5w[/tex]
Now we find out 'w' where area is maximum
[tex]w=-\frac{b}{2a} \\a=-1 and b=4.5\\w=-\frac{4.5}{2(-1)} =2.25[/tex]
Width =2.25 gives us maximum area
Now find out the length ,
[tex]Length = 4.5 -w\\w=2.25\\Length = 4.5-2.25=2.25[/tex]
Dimension of the picture is length = 2.25 ft and width =2.25 ft
Learn more : brainly.com/question/20977367
