Respuesta :
Here it is given that the width is x ft and total length of the fence is 2400 ft .
Let the length be y ft
So we have
[tex] 2(x+y) =2400 \\ x+y=1200 \\ y = 1200 -x [/tex]
Let A represents area, and area is the product of length and width .
So we get
[tex] A = x y [/tex]
Substituting the value of y, we will get
[tex] A = x (1200-x)= 1200x -x^2 [/tex]
Second part
The area is maximum at the vertex, and vertex is
[tex] x = - \frac{1200}{2(-1)} = 600 feet [/tex]
And
[tex] y=1200-x = 1200-600 = 600 feet [/tex]
And that's the required dimensions .
a) Area in terms of width x is given by
[tex]\rm Area = 1200x-x^2[/tex]
b) Dimensions of a rectangle are
length = 600 ft
width = 600 ft
Step-by-step explanation:
Given :
Length of fencing, F = 2400 ft
Solution :
Let width of ractangle be 'x' and length be 'y'.
Now. length of fencing is,
[tex]F = 2(x + y)[/tex]
[tex]2400 = 2(x + y)[/tex]
[tex]y = 1200 - x[/tex] ---- (1)
Now, area of rectangle is
[tex]\rm A = xy[/tex] --- (2)
From equation (1) and (2)
[tex]\rm A = x (1200-x) = 1200x-x^2[/tex]
a) Area in terms of width x is given by
[tex]\rm Area = 1200x-x^2[/tex]
b) For maximum area, we have to find A'
[tex]\rm A' = 1200 - 2x[/tex]
Now put A' = 0, we get
[tex]\rm x = 600 \;ft[/tex]
From equation (1) we get
[tex]\rm y = 600\; ft[/tex]
Therefore dimensions of a rectangle are
length = 600 ft
width = 600 ft
For more information, refer the link given below
https://brainly.com/question/17243806?referrer=searchResults
